The bathymetric mapping algorithm consists of three main steps (Fig. 2). Parameter initialization: Key input parameters for underwater elevation estimation, including the water mask and shore slope, are extracted from the updated SRTM Water Body Data (SWBD) and the NASADEM elevation bands. The water mask defines the spatial extent of the computation, while the shore slope serves as the independent variable for estimating underwater elevation. To better capture the representative shore-to-lake gradient, we estimate shore slope using a directional and robust scheme. Directional slopes are first computed along multiple orientations (eight-neighbor directions) and then rescaled within the buffer zone to match the magnitude range of a conventional 3 × 3-window slope map, thereby preserving directionality while reducing biases associated with single-direction calculations. Underwater elevation calculation: The water mask is treated as the initial lake surface. A simulated recession process is then applied, progressively lowering the water level and reducing the water mask coverage. This simulation process, initially proposed by Zhu et al. (2019), has been applied in recent studies. However, previous studies require manual predefinition of the water level drop at each step. In this study, the process is improved to automatically simulate the entire recession without manual intervention. A detailed description of the simulation process is provided in Sect. 2.2.2. At each step of the simulated retreat, elevation values for newly exposed underwater pixels are calculated. These elevations are estimated using a new profile-based underwater elevation model. This model adopts a quadratic function as the base form and defines an assumed lowest point based on the relative slopes of the two banks. Closed-form expressions then describe slope and elevation variations on both sides of this point, remaining applicable throughout the iterative drawdown. This iterative process continues until all pixels within the original water mask are assigned updated elevation values. Consequently, the original water surface elevations in the DEM are progressively replaced with estimated underwater elevations. Lake water storage estimation: The updated DEM, containing elevation values for underwater pixels, is combined with the lake extent to generate a complete bathymetric map. From this map, lake depth and water storage are calculated. This structured approach ensures accurate bathymetric mapping by iteratively estimating underwater elevations from shoreline topography and water level recession.

Three-dimensional visualizations of the simulated and in situ bathymetric maps (Fig. 6) were generated to compare their spatial patterns. The results demonstrate that the simulated bathymetry closely aligned with in situ water-depth measurements, accurately capturing variations in underwater terrain. Among all the sample lakes, Dong Co (Fig. 6c) exhibited the largest spatial discrepancy, likely due to its relatively flat shoreline, which limited the ability to infer underwater topographic patterns from the shoreline terrain. In contrast, Ngangla Rinco (Fig. 6i), with a more complex and fragmented shoreline, introduced localized inconsistencies in the simulated topography. As a result, the model tended to overestimate depths near the shore. Furthermore, as many salt lakes have expanded significantly in recent years, a noticeable discrepancy was observed between the in situ shoreline and the DEM-derived boundary. Therefore, the bathymetry near the shoreline – derived from the DEM in the transitional area between these boundaries – was observed to be less smooth than the in situ bathymetry.

To quantitatively evaluate the accuracy of the simulated bathymetry, we randomly generated 2,500 validation points within each lake boundary and compared simulated depths against in situ measurements. As shown in Fig. 7, the simulated depths exhibit good agreement with observations, with an average r value of 0.72 and an average NRMSE value of 19.09 %. Because the method assumes that nearshore topography contains informative signatures of underwater slope structure, its performance depends on the signal-to-noise ratio (SNR) of shoreline-derived slope information and the degree of structural coupling between shoreline morphology and lakebed geometry within a basin.

According to Table 2, the method underestimated maximum water depth for several lakes, including Angzi Co, Buruo Co, Longmu Co, Ngangla Rinco, and Taro Co. Among them, Ngangla Rinco (Fig. 7i) shows the weakest agreement. Inspection of the three-dimensional bathymetry (Fig. 6i) reveals an abrupt deepening in the southern part of the lake, indicating a localized bathymetric anomaly and partial shoreline–lakebed decoupling. Such features are difficult to infer from shoreline terrain alone, posing a challenge for approaches that rely primarily on nearshore topographic constraints. In contrast, simulated depths were overestimated for Dong Co and Mapang Yongco. In particular, Dong Co, with a surface area of 106.80 km² and a maximum depth of 3.99 m, exhibits relatively poor simulation performance despite its shallow depth. This likely reflects the limited depth range and the heightened influence of DEM noise and subtle topographic gradients, which can reduce the robustness of shoreline-derived slope signals and amplify relative errors.

Across all lakes, MAE is strongly correlated with lake depth (r=0.94). For deep lakes such as Buruo Co and Taro Co, where maximum water depths exceed 100 m, MAE values reached 17.33 and 21.15 m, respectively. This pattern suggests that shoreline–lakebed coupling tends to weaken with increasing depth, consistent with a reduced ability of shoreline-derived constraints to represent deep-basin morphology. Nevertheless, the model maintains acceptable accuracy across a wide range of lake sizes, depths, and morphologies, demonstrating its general applicability for regional-scale bathymetry estimation.

Lake water storage was calculated from the simulated bathymetric maps to further assess the effectiveness of the proposed method. For most lakes, the method yielded satisfactory water storage estimates (Table 2). The maximum water depth was derived as the maximum pixel value in the bathymetric map. It should be noted that in the simulated bathymetric maps, the location of the maximum depth pixel does not necessarily coincide with that in the in situ bathymetric map; nevertheless, the simulated deepest zone remains informative and provides a useful reference (Fig. S4). The PE between simulated and in situ bathymetric maps for Angzi Co, Buruo Co, Ngangla Rinco, Siling Co, and Taro Co remained within 10 %. Notably, despite a substantial underestimation of the maximum depth in Ngangla Rinco, its overall lake water storage estimate remained accurate. This result can be attributed to the offsetting effects between localized overestimation and underestimation in the simulated depth distribution. In contrast, Dong Co exhibited a large discrepancy in lake water storage estimates, with a PE of 94.84 % compared to the water storage derived from in situ bathymetry. This high error likely stemmed from the lake's shallow depth and small water storage, making it highly sensitive to even minor elevation errors. Despite the underestimation of maximum depth in Angzi Co, Buruo Co, Longmu Co, and Taro Co, the water storage estimates for these lakes remained reliable. This was because the overall depth distributions across the lake surface closely matched the in situ data, as illustrated in Fig. 7. In summary, among the 12 sample lakes, 10 exhibited water storage estimation errors below 30 %, including eight below 20 %, demonstrating that the proposed method performs well in most cases.

To assess the effectiveness of the proposed method for simulating underwater topography, Fig. 8 compares simulated and measured depth profiles along designated transects for 12 lakes. Each transect was carefully selected to align closely with the original depth survey routes while remaining near the lake center to ensure representative and consistent validation (Fig. S5). The average NRMSE across the 12 transects was 27.34 %, and the average MAE was 10.94 m, indicating an overall acceptable level of accuracy. In general, the simulated profiles were highly consistent with in situ measurements, effectively capturing the overall trends in depth variation. When transects extended toward lake shores, the simulated elevation gradients matched the in situ measurements well, demonstrating the method's capacity to represent shoreline-to-bottom topographic transitions accurately. However, deviations were observed near the lake bottoms in several cases. Simulated depths were overestimated in Angzi Co (Fig. 8a), Buruo Co (Fig. 8b), Mang Co (Fig. 8g), and Taro Co (Fig. 8l), while underestimations occurred in Dong Co (Fig. 8c) and Mapang Yongco (Fig. 8h). In other cases – such as Longmu Co (Fig. 8f), Ngangla Rinco (Fig. 8i), and Salt Lake (Fig. 8j) – although the general profile trends aligned well with observations, the method struggled to capture localized anomalies on the lake bottom. These discrepancies are likely linked to the complex geomorphological evolution of lakes on the Tibetan Plateau, which has experienced expansion, contraction, and migration processes over time. Such dynamic processes have resulted in heterogeneous sediment deposition and irregular bathymetric features (Yu et al., 2019). Consequently, a single correction formula may not fully account for the diverse morphologies of lakes. Despite these challenges, the proposed method demonstrates robust performance in simulating lake depth and bathymetry, supporting its applicability across varied lake environments.

The simulated lake water storage for the 12 sample lakes was compared with results from three previous studies (Table 3). For the GLOBathy dataset, absolute percentage error (APE) of lake water storage estimates ranged from 1.79 % to 324.93 %, indicating considerable variability, with nearly half of the lakes exhibiting errors greater than 50 %. In contrast, the dataset generated by Han et al. (2024) had an APE range of 0.52 % to 375.20 %, with four lakes showing APEs below 30 %. The large errors in GLOBathy are primarily attributed to limitations in its bathymetry reconstruction method and uncertainties in estimating maximum depth. Although Han et al. (2024) proposed an ICESat-2-based bathymetry reconstruction method, their dataset was derived from empirical equations. When applied to individual lakes, these equations can introduce unpredictable errors that may account for the observed inconsistencies. Moreover, among the nine overlapping sample lakes reported in Fang et al. (2023), the average APE was 31.80 %, outperforming both GLOBathy and Han et al. (2024). In comparison, our method achieved an average APE of 27.14 % across the same nine lakes. Furthermore, among all 12 sample lakes, only Dong Co, Guomang Co, and Mapang Yongco exhibited PEs greater than 30 %. These findings suggest that our method provides more accurate and robust lake water storage estimates compared to existing datasets.

In the comparative analysis, as the water storage estimates from Han et al. (2024) were available only through 2022, the corresponding water surface extent and water level for that year were extracted, and the in situ water storage data were aligned to the same period for consistency. Since the water surface extent in GLOBathy's bathymetric maps was derived from HydroLAKES, the lake water storage estimates from GLOBathy were also adjusted to reflect the conditions in 2022. It should be noted that the boundary defined by the measured bathymetric data (depth = 0 m) was considered the lake shoreline in this study. Due to limitations in the bathymetric survey equipment, measurement uncertainties may exist within the recorded depth range.

We evaluated the effects of different input DEM datasets on water depth simulation and found that the resolution and quality of the input data significantly affect the simulation performance (Fig. 9). Overall, simulations based on NASADEM achieved the lowest mean APE, followed by MERIT DEM and ALOS PALSAR. The detailed evaluation results for ALOS PALSAR and MERIT DEM are presented in Tables S1 and S2, respectively. In addition, the error distributions for NASADEM and MERIT DEM were more compact, indicating greater stability compared to the more dispersed errors observed in ALOS PALSAR-derived results. While increasing DEM resolution from 90 to 30 m clearly improved simulation accuracy, further refinement to 12.5 m using ALOS PALSAR unexpectedly reduced accuracy. Although recent studies have demonstrated the high vertical accuracy of ALOS PALSAR over the Tibetan Plateau (Xu et al., 2024), its performance in water depth simulation within our methodological framework was inferior to that of NASADEM. This discrepancy may be attributed to a combination of the intrinsic data quality and the simulation algorithm's sensitivity to varying spatial resolutions, which together could explain the suboptimal performance of ALOS PALSAR in this context. Beyond spatial resolution, the DEM acquisition time is also critical for our method. Because the algorithm infers underwater elevations from shoreline gradients and a DEM-derived water mask, DEMs acquired at lower lake levels can preserve more exposed nearshore topography. This additional geomorphic information strengthens constraints on shoreline-slope estimation and the subsequent recession simulation. In this regard, the earlier acquisition time of NASADEM may partly explain its better performance compared to ALOS PALSAR, despite the latter's finer spatial resolution.

We compared simulated maximum depth and water storage for the 12 sample lakes using input datasets with different spatial resolutions (Table S4). Two moderately sized lakes (approximately 100 km²) with reliable simulation performance were selected to examine spatial variations in depth estimates across datasets. Overall, the bathymetric maps generated at 12.5 m (Fig. 10b, f) and 30 m (Fig. 10c, g) resolutions exhibited broadly consistent spatial patterns. In contrast, the simulated bathymetry based on the 90 m-resolution DEM (Fig. 10d, h) showed a pronounced underestimation of depth across the entire domain, consistent with the quantitative results for depth and water storage (Table 4). This bias arises because the proposed method operates at the pixel level, and coarser resolutions smooth shoreline elevation, leading to an underestimation of the slope factor during the “parameter initialization” step. Consequently, coarser-resolution inputs produce gentler underwater topography, but this results in substantial depth underestimation in deep-water areas compared with in situ measurements. Increasing the resolution from 90 to 30 m markedly improves the representation of deep-water areas, while further refinement to 12.5 m yields no notable change in spatial patterns. Therefore, considering both computational cost and accuracy, a 30 m input resolution is optimal for the proposed method.

We further assessed how bathymetric accuracy responds to the distance of the dynamic exposed area used to calculate shoreline slope by testing maximum buffer widths of 300, 600, and 900 m (Fig. 11). The median NRMSEs are similar across the three settings (16.65 %, 18.00 %, and 18.14 %, respectively), indicating that overall performance is not strongly sensitive to buffer width within the tested range. However, error dispersion increases with buffer size, with the 900 m setting exhibiting the largest interquartile range (IQR = 7.72) and a more pronounced upper tail. This suggests that overly wide buffers may incorporate broader-scale topographic signals unrelated to the representative nearshore slope (e.g., terraces or distant hillslopes), thereby degrading performance for some lakes. In contrast, the 600 m setting yields the smallest IQR (6.19) and the most consistent results across lakes; it is therefore adopted as the default in this study. Notably, because our workflow determines an adaptive buffer extent using the multi-level buffering scheme described in Sect. 2.2.1, the specified value represents the maximum buffer distance and is not necessarily reached for all lakes. In some cases, the optimal buffer is identified at a shorter distance, so the maximum value is not applied.

To evaluate the applicability of the proposed method, we conducted a case study on Lake Mead in the United States (36.25° N, 114.39° W). As an artificial reservoir, Lake Mead differs significantly from the natural lakes analyzed in this study. Being a river-type reservoir, its underwater topography exhibits significant spatial heterogeneity across different sections of the river channel. Moreover, unlike many lakes on the Tibetan Plateau, which are characterized by thick sediment layers, sediment deposition in Lake Mead is primarily concentrated within the central river channel (Fig. 12c), resulting in a relatively flat underwater terrain (Rosen and Van Metre, 2010). To account for these characteristics, the sediment correction module was applied selectively – targeting only the central portion of the profile – during simulation. This tailored approach enabled the generation of a bathymetric map for Lake Mead (Fig. 12b) that more accurately reflects its distinct geomorphological features.

The simulated underwater elevation map (Fig. 12a) showed an overall consistent pattern and morphology with the in situ bathymetric map (Fig. 12b). The error distribution was predominantly centered around zero, although localized areas of noticeable overestimation and underestimation were evident (Fig. 12c). Overestimations primarily occurred in the sediment-rich areas, which correspond to the original pre-impoundment riverbed. In these regions, applying the correction formula from Eq. (6) led to an underestimation of the slope, thereby contributing to the overestimated elevations. To quantitatively assess the simulation accuracy, 2500 validation points were randomly selected across the entire lake, and the results were visualized in a scatter plot (Fig. 12d). The results revealed a strong correlation between in situ and simulated water depths (r=0.66). A significant concentration of validation points was observed at elevations above 300 m, while point dispersion amplified with decreasing elevation, indicating greater uncertainty at deeper sections of the lake. Overall, simulation performance tended to degrade with increasing depth. Despite these challenges, the results demonstrate that the proposed method has promising potential for application in lakes and reservoirs across diverse environmental conditions and geomorphological settings.