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1. Discover Geoscience Richardson et al. Discover Geoscience (2025) 3:103 https://doi.org/10.1007/s44288-025-00219-1 Open Access RESEARCH A case study comparing approaches to mask satellite-derived bathymetry Galen Richardson1*, Anders Knudby1, Yulun Wu1 and Mohsen Ansari1 *Correspondence: Galen Richardson galen.richardson@uottawa.ca 1Department of Geography, Environment and Geomatics, University of Ottawa, 60 University Private, Ottawa, ON K1N 8Z4, Canada Abstract Satellite-derived bathymetry (SDB) is a cost-effective method for estimating water depth in inland and coastal waters, but is only applicable to optically shallow water (OSW). Determining the appropriate extent of SDB maps and the depth threshold for accurate SDB model predictions has therefore been a challenge for practical applications of SDB. Previous studies have used either a numeric cut-off value or manually delineated OSW to determine where to apply, and where not to apply, SDB models. We compared the use of a threshold applied to the predicted depth, automated delineation of OSW using a published model, and manual delineation of OSW, to determine which method of masking unsuitable pixels for SDB performs best. We used a water-leaving reflectance Sentinel-2 image of the St. Lawrence River, and a Random Forest model using neighbouring pixel information to predict SDB. We then compared the different approaches to masking unsuitable pixels in terms of the mean absolute error (MAE) of the retained predictions and the total mapped area. The application of a model-predicted depth threshold is easy to implement and achieved an MAE of 0.54 m, outperforming automated and manual OSW delineation methods, which had MAEs of 1.39 m and 1.64 m respectively over an approximately 100 km2 study area. Future studies should further investigate these and other methods for masking pixels unsuitable for SDB under a wider range of environmental conditions. Keywords Satellite derived bathymetry, Predicted depth threshold, SDB, Random Forest, Sentinel-2, St. Lawrence river 1 Introduction Accurate and up-to-date bathymetric data are essential for a wide range of applications, including navigation, coastal engineering, habitat mapping, and climate change adap- tation. Traditional bathymetric survey methods, using shipborne sonar and airborne LiDAR, provide high-precision measurements but are costly and logistically challeng- ing, particularly in dangerous, remote or dynamic environments [1]. Satellite-derived bathymetry (SDB) has emerged as a cost-effective alternative, leveraging optical remote sensing to estimate water depth in shallow coastal and inland waters [2–5]. By quantifying the relationship between water depth and pixel reflectance in a satellite image, SDB can provide wide-area coverage at a relatively low cost and with frequent © The Author(s) 2025. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

2. Richardson et al. Discover Geoscience (2025) 3:103 Page 2 of 11 updates [6]. This makes SDB particularly useful for monitoring dynamic environments where frequent bathymetric updates are required, e.g. to ensure safety of navigation in areas where shoals may rapidly change location, to understand sediment dynamics and shoreline evolution, or for hydrologic modeling and flood preparedness. However, the accuracy of SDB-derived water depth estimates is inferior to that of tra- ditional survey methods and varies depending on factors such as water clarity, seafloor composition, and image quality. Importantly, the depth of water itself strongly influences how accurately it can be estimated by SDB; accuracy is typically highest in shallow water and gradually decreases with increasing depth until a limit is reached beyond which SDB cannot produce meaningful water depth estimates (e.g [7–9]). This limit exists since SDB can only provide useful water estimates in optically shallow water (OSW), where light reflected off the bottom has a detectable influence on the signal measured by the satellite sensor, and by extension where a relationship exists between water depth and pixel reflectance [5]. Ensuring that SDB-derived depths are limited to areas where they are meaningful and sufficiently accurate is therefore crucial, and it is important in any application of SDB to identify and limit the water depth estimates to areas where their accuracy meets the required standards for a given application, i.e. where they are fit for purpose. The need to constrain SDB-derived water depth estimates to areas where they meet accuracy requirements is widely recognized, and a range of approaches are used to accomplish this task. These include delineation and masking of optically deep water using visual image interpretation [10], sometimes aided by image segmentation and seg- ment classification [8, 11], or using mathematical or machine learning models [2, 12– 14]. Other approaches apply a depth threshold, masking out any SDB estimation deeper than a certain depth [15–17], often without justification for how this depth threshold was identified [18–20]. Alternative ideas include masking deep water based on the stan- dard deviation of SDB predictions from multiple images [21] or using radiative transfer- based simulations [22]. Many SDB studies published in the academic literature ignore this practical consideration and simply produce SDB estimates for every pixel in the sat- ellite image (e.g [7, 24–27]). No study that we are aware of compares different approaches to such masking for applied SDB, the advantages and disadvantages of different approaches are rarely con- sidered, and justification for the use of any given approach is rarely provided. This is problematic because a fundamental trade-off exists between the spatial coverage of SDB-derived water depth estimates and the accuracy of those estimates. If high accuracy is prioritized, then the extent of SDB maps must be restricted to areas where the model performs well at the task of predicting water depth. In this study, we tested and com- pared three different approaches to defining where SDB models are suitable, using water depth estimates produced from a Random Forest (RF) SDB approach applied to a Sen- tinel-2 image from a portion of the St. Lawrence River. By comparing these approaches, both in terms of the accuracies they result in and the area for which they allow water depth estimates to be produced, we aimed to provide insights into the advantages and disadvantages of each approach, to guide SDB practitioners and inspire additional research into the development of approaches that optimize the trade-off between areal coverage and accuracy.

3. Richardson et al. Discover Geoscience (2025) 3:103 Page 3 of 11 2 Methods 2.1 Study area The area of interest was an approximately 100 km2 portion of the St. Lawrence River, North of Varennes and South of Sorel-Tracy, Québec, where there has been a proposal for the expansion of the Contrecoeur Terminal (Fig. 1). The St. Lawrence River is often turbid as a result of suspended sediment and contains patches of seagrass, making this region generally challenging for SDB. However, the spatial heterogeneity of this optically complex area also makes it interesting for assessing different methods of determining where SDB models are and are not suitable. 2.2 Imagery A Sentinel-2 image captured on September 16, 2024, was used for SDB in this study since it was cloud-free and the study area had relatively low turbidity compared to what is observed in other images. We used Sentinel-2 bands 1–5, resampled as required to 10 m, since all other bands record wavelengths that are absorbed effectively by water and contain little information about water depth [5]. The Sentinel-2 image was processed using ACOLITE (version 20231023.0) to derive water-leaving reflectance (RWL); ACO- LITE has been shown to perform well over coastal and inland waters [28–30]. 2.3 Sonar data Data from boat-based acoustic surveys were used for model calibration and evalua- tion (Fig. 2). We used data from five surveys conducted by the Canadian Hydrographic Society (CHS) in 2023 and 2024 using the R2Sonic multibeam sensor, and 11 surveys conducted by WSP and the University of Ottawa in 2024 using the SonarMite BTX sin- gle-beam sensor. All surveys were conducted between the end of May to mid-Septem- ber to minimize the influence of winter meltwater. For all locations, including instances where SDB surveys overlapped, the bathymetric data were aggregated for every Senti- nel-2 (10 m) pixel and averaged, resulting in a single bathymetric raster at 10 m resolu- tion. This resulted in a dataset of 20,997 data points for model calibration and evaluation. 2.4 Dataset creation We sampled the image-derived RWL values at the locations of the 10 m bathymetric pix- els for model training. Previous research has shown that including neighbouring pixel information can improve SDB model performance [5, 31, 32]. Therefore, in addition to Fig. 1 The area of interest and the Sentinel-2 image used in this study

4. Richardson et al. Discover Geoscience (2025) 3:103 Page 4 of 11 Fig. 2 Locations of bathymetric data (red) used in this study (A) and the spatial blocking strategy used to minimize information leakage (B) the per-pixel values, we also included kernel averages for Sentinel-2 bands 1–5 at all bathymetric pixels, using the kernel sizes 3, 5, 7, 9, 11, 13, and 15. To minimize the influ- ence of information leakage between the training and evaluation datasets, we imple- mented a spatial blocking strategy consisting of 1-km2 blocks that were separated into five different groups [5, 33]. These groups of blocks were used for a five-fold cross-val- idation strategy, where models were calibrated on four groups (80%), and the remain- ing group (20%) was used for model evaluation [34, 35]. All groups were iteratively used for evaluation once, so that the model performance was assessed on the entire dataset. On completion of the model evaluation, all five groups (100%) were used to train a final model to produce bathymetric maps. 2.5 Model assessment We used a Random Forest (RF) regression model from the scikit-learn Python pack- age to predict water depth [36, 37]. RF is an algorithm based on multiple decision trees which are each optimized using a bootstrap sample of input data and a random sub- sample of predictors [36]. The water depth predictions are calculated as the mean value of the predictions from each decision tree in the forest. RF models have previously been used in SDB studies and are especially effective when using neighbouring pixel informa- tion [5, 32, 38, 39]. RF models tend to outperform parametric models developed from radiative transfer considerations [5, 9], and they can be calibrated and evaluated quickly, while more complex machine learning models, such as neural networks, are substan- tially more onerous to train and often perform similarly at this task [5, 6, 32, 39]. We tuned the RF number of trees (30, 100, 300, 1000) and the number of predictors considered in each feature (“auto”, “sqrt”, “log2”) and left the remaining parameters at their default value. Every combination of parameters was used for the five-fold cross-val- idation, and an average mean absolute error (MAE) value was calculated using the pre- dicted depths for all pixels in the dataset. The combinations of parameters that offered the lowest MAE for all pixels in the datasets were selected as the optimal model and used for the creation of SDB maps.

5. Richardson et al. Discover Geoscience (2025) 3:103 Page 5 of 11 2.6 SDB masking comparison We tested three different approaches to masking out deep water from the SDB maps. Given typical water quality in the study area, we estimated 5 m as an absolute upper limit for the bottom to be detectable, and thus for SDB predictions to be meaningful. 1) Model-predicted depth threshold. One approach to limit SDB maps to areas where they are considered fit for purpose is to define a maximum tolerable error and mask out predictions at depths where this error is exceeded. We defined this maximum tolerable error as MAE = 1 m; other values could be defined depending on application context or survey requirements, such as IHO standards [40]. We then calculated MAE values for predictions in 0.5 m intervals up to 5 m (i.e. 0–0.5 m, 0.5–1 m, … 4.5–5 m) to determine the deepest depth interval for which MAE < 1 m. This depth threshold was then applied as a mask by removing all deeper SDB predictions. 2) Manual delineation. As an alternative, we manually delineated OSW using visual inspection of the Sentinel-2 image (conducted by GR), digitizing polygons for areas where the river bottom was visually detectable in the image (OSW). SDB predictions were then removed from all other areas [10]. 3) Automatic delineation. Finally, we used a published tool (henceforth OSD; [41]) to predict the probability of each pixel being optically shallow, and masked out all pixels with this probability being < 50%. For each approach, the MAE, RMSE, and the number of unmasked bathymetric predic- tions were calculated, and maps were produced for visual comparison to the sonar data. For all maps in this study, non-water was masked out using the same filters used in the OSD tool [41]. 3 Results 3.1 SDB model performance The optimal RF model had 100 trees and used ‘log2’ to determine the number of predic- tors. A heatmap of the predicted and actual depths for the RF model showed a strong relationship with a slight overestimation of water depth (many points located above the white 1:1 line), and a few outliers that substantially overestimate depths under 1 m (Fig. 3). The model had MAE and RMSE values of 1.30 m and 1.96 m, respectively, when evaluated for the full depth range. The depth-disaggregated MAEs (Fig. 4) demonstrate that the RF model had acceptable performance (MAE < 1 m) up to and including the 2.0–2.5 m depth interval, with errors gradually increasing from the 1.0–1.5 m range (MAE = 0.38 m) through to the 4.5–5.0 m range (MAE = 1.96 m). 3.2 Comparison of SDB masking approaches Manual delineation of the visible river bottom took approximately four hours for the entire study area, while the processing time for the automatic delineation was 24 min on a desktop computer using an Intel i5-12600k. Applying the 2.5-m threshold to the SDB map was nearly instantaneous in a Python environment. When limiting the predicted depths to 2.5  m, model performance was substan- tially improved compared to no thresholding, with MAE and RMSE values of 0.54 m and 1.11 m respectively (Table 1). These results are consistent with the plot of depth- disaggregated MAE values (Fig. 4), where the model MAE is < 0.5 m at depths below

6. Richardson et al. Discover Geoscience (2025) 3:103 Page 6 of 11 Fig. 3 Comparison of predicted and actual depths for the RF model. Brighter pixels indicate a higher frequency than darker pixels Fig. 4 MAE per 0.5-m depth interval for the RF model Table 1 Comparison of SDB masking methods and their respective MAE, RMSE, and counts SDB Masking Method None Predicted depth threshold (2.5 m) Manual delineation of OSW Automatic delineation of OSW MAE 1.30 m 0.54 m 1.64 m 1.39 m RMSE 1.96 m 1.11 m 2.65 m 2.16 m Count 20,997 7744 5541 10,560

7. Richardson et al. Discover Geoscience (2025) 3:103 Page 7 of 11 1.5 m. Both manual and automatic delineation of optically shallow water yielded MAE values larger than 1 m, substantially greater than the predicted depth threshold method (Table 1). Of the pixel filtering methods, the automatic delineation of OSW resulted in the largest number of retained pixels, while the manual delineation of OSW had the few- est number of remaining pixels. Figure 5 illustrates the depth-disaggregated model per- formance over 0.5 m depth intervals up to 5 m, with both the automatic and manual masking approaches having acceptable performance (MAE < 1 m) up to the 1.5–2.0 m interval. Additionally, Fig. 5 displays the number of pixels for which an SDB prediction was retained (counts) for each SDB masking approach (grey bars). While all pixels using the predicted depth threshold of 2.5 m fall within depth intervals with acceptable per- formance, many of the pixels in the automatic and manual delineation methods are in intervals with poorer performance (MAE > 1 m). Therefore, the model-predicted depth threshold method not only provided a substantially lower MAE than other SDB masking methods, but it also provides consistently acceptable model performance for all depths retained. The predicted SDB map was masked using the three different SDB masking methods for visual inspection and comparison (Fig. 6). Both automatic and manual delineation methods allowed for predictions along the entirety of the riverbanks in the study area, whereas the predicted depth threshold (2.5 m) did not have predictions near all of the riverbanks. The automatic delineation had substantially more predictions greater than 2.5 m than the other methods. However, given the poor model performance of water depths greater than 2.5 m, both the manual and automatic methods contained pixels with presumably low accuracies. Fig. 5 MAE and count per 0.5 m depth interval for the three SDB masking approaches. The grey bars represent the count of predictions per depth interval

8. Richardson et al. Discover Geoscience (2025) 3:103 Page 8 of 11 Fig. 6 SDB maps for the predicted depth threshold (2.5 m), manual, and automatic SDB masking methods 4 Discussion The purpose of this study was to create an SDB model for an approximately 100 km2 portion of the St. Lawrence River and to compare three methodologies for masking the resulting SDB maps. While masking removes areas that still contain some information, it is essential for creating bathymetric maps that the user can have a given level of con- fidence in. Applying a threshold to model-predicted depths can create SDB maps that adhere to performance requirements and is easy to implement since it only requires numeric calculations with the validation dataset. For this type of delineation, the model’s performance itself is used to determine the depth range for which SDB predictions will be retained, and is an efficient approach to ensure that error metrics such as MAE or RMSE do not exceed performance requirements. However, it ignores any environmental factors that may influence local model performance. For example, dark substrates (e.g. seagrass) tend to produce greater SDB errors than light substrates (e.g. sand) for the same predicted depth range, something that this approach is unable to take into account [5]. Future studies should investigate whether a multi-task SDB and seafloor classifica- tion approach could improve model performance (e.g [42]). The other methods for masking SDB maps tested here, manual and automated delin- eation of optically shallow areas, produced substantially poorer overall performance as quantified by the MAE of the retained predictions. The automated delineation retained more SDB predictions than the model-predicted depth threshold approach, including at deeper depths, which explains the higher MAE value of this approach. The manual delineation approach performed poorly in both aspects - it retained SDB predictions for the smallest number of pixels and produced the highest MAE value of any of the

9. Richardson et al. Discover Geoscience (2025) 3:103 Page 9 of 11 approaches. Additionally, biases from the analyst (GR) who annotated OSW could have influenced the performance of manual delineation. It is important to note that this study was conducted in a complex river environment with limited OSW pixels located near riverbanks. Future studies should investigate whether the model-predicted depth threshold approach is also superior to the alternatives in other environments for which SDB is more commonly used. In addition to the RWL imagery used here, we also evaluated the use of top-of-atmo- sphere (RTOA) data, as well as a dataset with water-leaving reflectance corrected for the adjacency effect (RWLA) with T-Mart version 2.4.5 [43]. For both these alternative datas- ets, we optimized RF models as explained above and found that they performed similarly to the RWL model. Future improvements in SDB along the St. Lawrence River could be achieved by using more complex machine learning models such as a convolutional neural network (CNN). Previous studies have shown that CNN models can outperform other machine-learn- ing models for SDB [5]. However, CNN models were not considered due to the small number of sample points in this study (n = 20,997), the difficulty involved with imple- menting cross-validation methodologies for these model types, and the intensive trial- and-error period required to optimize model structure. Such models should be tested if the expected marginal gains are considered sufficiently important. 5 Conclusion We compared three different approaches to mask out SDB predictions in the St. Law- rence River, using RWL Sentinel-2 imagery and an RF model. The use of a threshold (2.5 m) applied to the predicted depths, defined based on the deepest depth interval for which MAE was < 1 m, provided the best performance with the lowest MAE and an acceptable number of SDB predictions retained. The use of manually or automati- cally defined masks to remove SDB predictions from optically deep water resulted in substantially higher MAE values for the retained predictions, and were therefore consid- ered inferior approaches. Furthermore, applying a model-predicted depth threshold is easier and faster to implement into SDB workflows than other forms of masking. Future research should further test these and other competing approaches to SDB masking for environments in which SDB is more commonly used. Acknowledgements The authors would like to acknowledge the Canadian Space Agency for the financial support under the SmartHarbour initiative, implemented in collaboration with Public Services & Procurement Canada and the Montréal Port Authority to foster the development and adoption of best practices for environmental monitoring as well as the protection of terrestrial and aquatic ecosystems. Additional support was provided by WSP, the Mitacs Accelerate program, and members of the University of Ottawa’s Shallow Water Earth Observation Laboratory. Assistance from ChatGPT-4o was used for portions of code development (e.g. code structure and debugging) and improving readability (e.g. text editing and word suggestions). All outputs were reviewed and edited by the authors as needed. Author contributions Galen Richardson: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing – original draft. Anders Knudby: Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Supervision, Writing – review and editing. Yulun Wu: Resources, Data curation, Software, Writing – review and editing. Mohsen Ansari: Resources, Data curation, Writing – review and editing. Funding This study received financial support from the Canadian Space Agency under the SmartHarbour initiative and the Mitacs Accelerate program (IT40023). Data availability The datasets generated during and/or analysed during the current study are not publicly available since they contain privately collected data but are available from the corresponding author on reasonable request.

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