This study focuses on beaches across New Zealand (approximately 166–179° E, 34–47° S). Located at the tectonic boundary between the Pacific and Australian plates, New Zealand is an island nation with an extensive coastline of approximately 15 000 km (Hamling et al., 2022). Its unique geological setting, combined with wide climatic variation from subtropical to temperate zones, has created highly diverse beach systems, making the country an ideal natural laboratory for coastal geomorphology research at the national level. Notably, New Zealand's coastal zones are relatively less disturbed by intensive human activities compared to many other populated coastal regions, allowing for the capture of natural beach topographic dynamics with minimal anthropogenic interference. Additionally, the country boasts comprehensive and openly accessible datasets, including high-precision airborne Lidar DEMs (Land Information New Zealand, LINZ), long-term Sentinel-2 satellite imagery, and detailed coastal geographic information (OpenStreetMap, OSM), which provide robust data support for large-scale topographic reconstruction. These beach systems are subject to frequent tidal inundation and periodic exposure driven by dynamic marine processes. Consequently, extensive intertidal zones are formed where the land-sea interface is constantly shifting due to the rise and fall of the tides. In addition, coastal zones in New Zealand are facing growing challenges, including sea-level rise and intensified coastal erosion, underscoring the critical need for accurate, high-resolution topographic reconstruction and monitoring. The study area overview is shown in Fig. 1.

This study also incorporated coastal geographic information from OSM (https://osmdata.openstreetmap.de/, last access: 15 October 2025), including coastline, land surface, and beach surface datasets. The coastline data were used to define the land–sea boundary to provide the spatial basis for calculating geometric features. The land surface data were employed to identify terrestrial regions and assist in the generation of coastal buffer zones. The beach surface data were utilized to delineate the spatial extent of beaches and to guide data filtering and model application. Together, these ancillary datasets provided essential geographic context, supporting the accurate identification of beach areas and the quantitative characterization of their spatial attributes.

A comprehensive evaluation framework was established to assess both the predictive behavior of the machine learning model and the accuracy of the final applied beach topography. The first part of the evaluation focused on point-level predictive performance using the ICESat-2 median elevation samples. Independent training, validation, and test datasets were used to quantify the model's learning and generalization behavior. The second part was a comprehensive accuracy validation of the results of this study based on the Lidar DEM, which includes point-level accuracy validation, profile and spatial accuracy validation (assessed at 6 beaches), and cross-beach transferability validation. To quantify accuracy, this study employed four metrics, namely the coefficient of determination (R2), RMSE, MAE, and mean bias error (MBE). Their calculation formulas are provided as follows. 2R2=1-∑i=1nyi-y^i2∑i=1nyi-y‾23RMSE=1n∑i=1n(yi-y^i)24MAE=1n∑i=1nyi-y^i5MBE=1n∑i=1nyi-y^i among these variables, yi represents the measured elevation value from ICESat-2, y^i denotes the model-predicted elevation value, y‾ is the average of the measured values, and n stands for the number of samples. By comparing these metrics across the training set (reflecting model fit), validation set (reflecting model tuning effectiveness), and test set (reflecting model generalization), we can systematically diagnose whether the model suffers from overfitting or underfitting and confirm its robustness.

To ensure the representativeness and validity of profile and spatial accuracy validation, the 6 random beaches used in this process were selected by stratifying New Zealand's North and South Islands (3 each) to cover coastal topographic diversity, with strict requirements for complete airborne Lidar DEM coverage to enable high-precision reference comparison and sufficient predicted pixels to focus on the study's core supplemented topography. The detailed information of these 6 beaches is shown in Table 3.

To interpret the predictions of the optimized XGBoost model and to quantify the relative importance of input variables in predicting beach elevation, we employed the SHAP (SHapley Additive exPlanations) framework (Lundberg, 2017). SHAP is a framework derived from cooperative game theory that attributes each model prediction to the contribution of individual input features by distributing the prediction value among them in a theoretically consistent manner. This method provides an intuitive and model-agnostic approach for understanding how different features influence the predictions.

In this study, SHAP values were calculated using all samples from the independent test dataset, which had not been used during model training. The SHAP computation was carried out in Python 3.11 using the TreeExplainer algorithm, which is specifically designed for tree-based ensemble models such as XGBoost. This procedure provides a transparent and data-driven interpretation of how spectral and geometric features influence beach elevation predictions.

The goal of this study is to generate a seamless national-scale beach topographic product by effectively bridging the persistent data gaps in the existing baseline. To achieve this, a targeted fusion strategy was adopted that integrates the high-precision backshore topography from DeltaDTM with our reconstructed intertidal topography.

The specific workflow involved two main stages. First, the preprocessed Sentinel-2 spectral features and geometric features (17 in total) covering the national beach areas were input into the trained and optimized XGBoost model. This step focused specifically on the regions identified as “NoData” in DeltaDTM and generated pixel-level elevation predictions exclusively for the missing intertidal and foreshore zones. Second, these predicted elevations were seamlessly mosaicked with the valid DeltaDTM pixels. By treating DeltaDTM as the accurate “skeleton” for stable terrain and the ML predictions as the “connective tissue” for dynamic zones, yielding a single, continuous 30 m resolution digital terrain model. The final product extends from the backshore dunes to the underwater shoreface without altering the verified high-quality data in the baseline. Ultimately, a complete, continuous, and seamless digital terrain model spanning from the backshore to the underwater shoreface is formed.

Data balancing with the SMOGN algorithm effectively reduced systematic overestimation of low-elevation values and improved the overall distribution of predicted beach elevations (Fig. 3a–f). Before data balancing (Fig. 3a–c), the model tended to overpredict near-zero elevations, as reflected in the validation and test sets. In the test set, the mean bias error (MBE) reached 0.06 m, indicating a slight but consistent overestimation. After applying SMOGN (Fig. 3d–f), the number of training samples increased from 3074 to 5606, expanding the model's capacity to capture low-elevation cases. Consequently, the test-set MBE decreased from 0.06 to 0.00 m, confirming that the average bias was effectively corrected. The balanced model also produced predictions with a wider and uniform range, indicating improved representation of elevation variability across coastal zones.

Model accuracy remained satisfactory after balancing, maintaining sub-meter accuracy (i.e., RMSE) for both validation and test sets (Fig. 3d–f). Although the pre-balancing model achieved slightly better accuracy metrics, the balanced version yielded a more uniform distribution of predicted elevations and a more realistic depiction of terrain gradients. This trade-off slightly reduced precision but enhanced spatial consistency, which is preferable for regional-scale coastal terrain modeling. Given the sub-meter RMSE accuracy and the reduced prediction bias, the final model demonstrates strong practical utility for coastal terrain estimation in low-relief environments.

Comparison with airborne Lidar reveals that DeltaDTM systematically underestimates terrain elevation, particularly in low-lying coastal zones (baseline comparison, Fig. 4a). Relative to the Lidar DEM, DeltaDTM attains R2 = 0.59, RMSE = 1.37 m, MAE = 0.95 m, and MBE = -0.16 m (Fig. 4a). Its elevations are mainly concentrated between 2 and 6 m, indicating substantial data gaps in low-relief intertidal areas. In contrast, the ICESat-2 median values (overall range: -2 to 10 m) show good agreement with Lidar but exhibit a positive bias (MBE = 0.13 m) that may propagate into subsequent modeling, with overall metrics of R2 = 0.66, RMSE = 0.94 m, and MAE = 0.64 m.

To validate model performance in these data-void regions, accuracy was first evaluated specifically within the newly supplemented intertidal zones (Fig. 4f). Here, the SMOGN-balanced model achieved an RMSE of 0.94 m and an MAE of 0.70 m. This sub-meter accuracy confirms its capability to reconstruct topography in areas entirely absent from the baseline dataset. Prior to balancing, the model exhibited a positive bias (MBE = 0.23 m; Fig. 4d) in these regions, which was reduced to 0.16 m by the SMOGN algorithm.The final integrated product demonstrates robust overall accuracy. Across the entire study area (Fig. 4e), it attains R2 = 0.75, RMSE = 1.17 m, MAE = 0.82 m, and MBE ≈ 0 m. The close agreement between the newly predicted intertidal elevations and the baseline DeltaDTM backshore confirms a seamless integration. While the unbalanced model showed marginally higher scores on some metrics (Fig. 4c), the balanced model delivered more realistic terrain gradients and a smoother cross-shore transition. Among these validation results, the accuracy within the newly predicted intertidal voids (Fig. 4f; R2 = 0.61, RMSE = 0.94 m, MAE = 0.70 m) directly indicates the model's ability to reconstruct the topography originally missing from the DeltaDTM baseline. This sub-meter accuracy demonstrates the effectiveness of the gap filling approach. The combined product metrics for the entire study area (Fig. 4e; R2 = 0.75, RMSE = 1.17 m, MAE = 0.82 m) include the high quality DeltaDTM backshore pixels and therefore reflect the performance of the integrated product, not solely the machine learning prediction component.

Case studies at six beaches show that predicted spatial patterns match realistic coastal morphology, and their aggregated accuracy closely reflects overall model performance (Fig. 5). Pixel-level predictions (Fig. 5a–f) exhibit the expected inland-rising elevation gradients. Aggregated validation against Lidar across all six beaches (n= 16 342 pixels) yields R2 = 0.826, RMSE = 1.054 m, MAE = 0.744 m, and MBE = 0.186 m (Fig. 5g). The slightly positive MBE indicates regional variability, with some beaches showing localized overestimation. Residual analyses for individual beaches reveal location-dependent biases, though most pixel residuals are centered near zero (Fig. 6). The mean residuals for panels a–f are -0.182, +0.111, -0.240, +0.132, +0.637, and -0.077 m, respectively (Fig. 6). The highest mean deviation is observed in panel e (+0.637 m), and the smallest absolute bias in panel f (-0.077 m). Although minor beach-specific biases exist, most residuals cluster tightly around zero. This demonstrates that the model is largely unbiased at the pixel scale, with any systematic bias confined to specific localities. To validate the vertical gradient consistency of the dataset, we extracted cross-shore profiles perpendicular to the coastline for six representative beaches (FIDs 220, 222, 678, 343, 418, and 421). We conducted pixel-level elevation comparisons between NZ-BeachTopo30 and the Lidar DEM along these profiles as shown in Fig. 7g–l. To focus the assessment on the active beach zone, the comparison was strictly limited to elevation values ranging from -2 to 10 m. Crucially, the gray-shaded regions in the profile plots highlight the newly added areas, allowing for a targeted evaluation of the gap-filling performance. RMSE and MBE were calculated for each profile to quantify the agreement between the datasets. Among the six beaches, the profile for the beach with FID 222 (Fig. 7h) exhibits the highest agreement with the Lidar DEM, achieving an RMSE of 0.421 m and an MBE of -0.139 m (n= 15). The predicted elevation curve closely overlays the Lidar-derived curve, maintaining high consistency even within the newly filled intertidal segment. In contrast, the beach with FID 678 (Fig. 7i) shows the lowest profile accuracy, with an RMSE of 1.069 m and an MBE of 0.381 m (n= 9). Although the predicted profile exhibits a positive bias in this specific case, the overall rising trend still aligns with the Lidar reference. For the updated profiles of FID 418 (Fig. 7k) and FID 421 (Fig. 7l), the model also demonstrates robust performance, yielding RMSE values of 0.502 and 0.771 m, respectively. Overall, the average RMSE across all six profiles is approximately 0.71 m, indicating that the model effectively captures the cross-shore morphological gradients and successfully reconstructs the topography in the previously missing intertidal zones.

Our analysis reveals realistic elevation patterns across beach units, with mean-elevation classes concentrated in mid-range intervals (summary by beach polygon, Fig. 8). When mean elevation is classified into five categories (< 0, 0–1, 1–2, 2–5, > 5 m), statistical analysis reveals clear spatial variability in beach quantity proportions between New Zealand's North and South Islands, as well as consistent trends at the national scale. Nationally, mid-elevation beaches (1–2 and 2–5 m) dominate the distribution, while low-elevation beaches (< 0 and 0–1 m) are relatively scarce, and high-elevation beaches (> 5 m) account for the smallest share. The North Island shows a higher concentration of mid-to-high elevation beaches, whereas the South Island has a relatively larger proportion of low-elevation beaches, particularly in the 0–1 m interval, which reflects distinct topographic characteristics between the two islands. The inset boxplot in Fig. 8 further quantifies elevation distribution differences: the North Island's beach mean elevations are slightly higher than the South Island's, and the national median mean elevation clusters near 2 m, with the minimum elevation reaching approximately -1 m. This elevation pattern aligns well with the comparison results referenced in Fig. 4e, which exhibits a notable increase in low-elevation pixels (< 2 m). This consistency confirms that the model successfully reconstructs nearshore intertidal topography. The greater representation of low elevations in NZ-BeachTopo30 directly corresponds to these previously unrecorded intertidal zones, thereby filling the critical data gaps.

Systematic data gaps in coastal DTMs are predominantly concentrated in intertidal zones, where periodic tidal inundation masks low-elevation terrain from conventional sensors (Bishop-Taylor et al., 2019). To quantify the extent of coverage expansion and rigorously demonstrate the full-coverage advantage of NZ-BeachTopo30, we compared the spatial completeness of the baseline DeltaDTM against NZ-BeachTopo30. After projecting both datasets into the NZTM2000 coordinate system, Fig. 9b reveals a substantial expansion in coverage: the original DeltaDTM covers only 79.9 km², whereas the mosaicked DeltaDTM expands to 196.5 km². This adds approximately 152 935 new pixels, corresponding to an area of 116.6 km² – a 145.8 % increase over the baseline. Furthermore, Fig. 9a indicates that the number of covered beach units increased by 19.5 %, from 1319 to 1576.

Figure 9c compares the elevation distributions of the original DeltaDTM and the newly added pixels. The median elevation of the newly added pixels (∼ 1.5 m) is substantially lower than that of the original DeltaDTM (∼ 4 m). The first and third quartiles of the newly added pixels are concentrated at lower elevations, indicating that the model primarily fills gaps in low-elevation areas such as intertidal zones rather than in high-elevation areas. The interquartile range of the newly filled pixels is relatively narrow, which implies that these newly added values are clustered within the low-elevation segment.

Figure 9d compares the elevation histograms of the original DeltaDTM and the NZ-BeachTopo30 dataset. It shows a substantial increase in the total number of valid pixels after mosaicking, along with a marked increase in the low-elevation range. This pattern indicates that the model effectively predicted missing elevations in nearshore and intertidal zones, thereby improving data continuity in previously missing areas. While the high-elevation portion of the distribution remains largely unchanged, the low-elevation portion exhibits a distinct shift and broadening, reflecting the successful filling of low-lying gaps during the fusion process. Figure 10a illustrates the expansion in beach coverage at the beach-unit level. Beaches already covered by the original DeltaDTM are depicted in green, while those newly covered by the dataset are shown in red. The inset donut chart quantifies this relationship where 83.7 % of beach units had prior coverage in DeltaDTM whereas NZ-BeachTopo30 successfully introduced coverage to the remaining 16.3 % of beaches that were previously unmapped. Figure 10b further maps the magnitude of these intertidal supplements for individual beaches, classifying each beach into one of four bins based on the size of its newly added area. The inset donut chart presents the frequency distribution of beaches across these size classes. The results reveal that the majority of beaches (56.6 %) received only minor area supplements (0–0.01 km²), indicating that for most coastal units, the reconstruction primarily filled narrow intertidal fringes or small voids. However, a notable proportion (15.2 %) of beaches gained substantial area coverage (> 0.1 km²). This distribution suggests that while the gap-filling effect is ubiquitous across all beaches, our method is particularly vital for capturing the large intertidal zones of major beach systems that were largely absent from the baseline.

To evaluate the spatial transferability of the model to beaches without direct ICESat-2 coverage, a comparative accuracy assessment was conducted at the beach-unit level. For each beach, RMSE and MAE were calculated using only the newly predicted pixels within the intertidal/foreshore zone (elevation range: -2 to 10 m). These predictions were validated against the airborne Lidar DEM. Figure 11 illustrates the distribution of these error metrics, distinguishing between beaches that contained ICESat-2 training samples and those that did not.

As shown in the statistical summary, sites with ICESat-2 samples (n= 148) achieved mean RMSE = 0.93 m and MAE = 0.74 m. In comparison, beaches without samples (n= 223) had slightly higher errors (mean RMSE = 1.02 m, MAE = 0.85 m). Violin plots (Fig. 11a, b) further show that the group with training data has a tighter error distribution with fewer outliers, whereas the untrained group shows broader variability. Although local training data yields a measurable improvement in accuracy and stability, the performance gap is narrow. This demonstrates the model's robust cross-beach transferability, allowing effective reconstruction of intertidal gaps even where direct ICESat-2 data are absent.

Based on the computed SHAP values, three types of visualizations were generated to examine how the model uses input features for elevation prediction. The first is the SHAP summary plot, which simultaneously conveys feature importance and the direction of impact. Features are ranked in descending order of global significance, represented by their mean absolute SHAP values. Each point in the plot corresponds to a single sample; the color indicates the magnitude of the feature value, while the horizontal position denotes the direction (positive or negative) and strength of its contribution to the prediction. This visualization provides a global overview of the model's decision-making process. The second visualization is the SHAP feature-interaction heatmap, which illustrates the average interaction intensity between pairs of important features. This representation highlights synergistic relationships and helps elucidate the complex interactions that influence the model's predictive behavior. Finally, the SHAP dependence plot was used to investigate the effects of individual features further. For the six most important features identified in the summary plot, dependence graphs were generated to show the relationship between each feature's actual value and its corresponding SHAP value. These plots clearly reveal the nonlinear dependencies between single features and the model's predicted output.

High near-infrared (NIR) reflectance is strongly associated with higher predicted beach elevation (Fig. 12a). Among all predictors, B8_20p (the 20th percentile of the near-infrared band) contributes most positively to the model output. This is consistent with the physical principle of strong water absorption in the NIR spectrum, where high NIR values correspond to dry, exposed supratidal sands and low NIR values are characteristic of frequently inundated intertidal zones. Conversely, B3_20p (the 20th percentile of the green band) has the strongest negative effect. High green-band reflectance is typically associated with shallow water bodies or moist sediments in low-lying areas, which the model correctly interprets as indicators of lower elevation. Geometric and positional features such as In_dis, Coast_dis, Co_ratio, X, and Y also rank among the most influential variables. This indicates the model uses spatial context to enforce a realistic topographic structure, ensuring predicted elevations follow a plausible cross-shore geomorphological gradient.

The distribution of SHAP values across all samples (Fig. 12b) shows that B8_20p has a clear positive contribution trend, while B3_20p exhibits variable and opposing effects. This confirms that the model relies heavily on the moisture sensitive NIR band to resolve the primary elevation gradient from the sea to the land (Fig. 12b). Spatial and geometric features consistently show positive SHAP values, reinforcing their supportive role in refining the spatial continuity of the beach profile. The variability in SHAP values arises from the heterogeneity of coastal conditions, demonstrating that the model captures distinct spectral-topographic relationships across the backshore, foreshore, and intertidal zones.

Nonlinear feature responses (Fig. 12c) further illustrate how the model handles the intertidal interface. B8_20p exhibits a sharp monotonic increase in SHAP values at lower reflectance ranges before stabilizing at high levels. This steep rising segment precisely corresponds to the transition from the wet intertidal zone to the dry backshore, demonstrating that the model is highly sensitive to moisture changes in this critical gap region. In contrast, B3_20p displays a pronounced negative trend that levels off at moderate reflectance, confirming its association with low-lying wet areas or shallow water. In_dis shows a nonlinear response with substantial variability, reflecting the complex morphological transition between landward and seaward beach zones. B8_50p follows a positive trend similar to B8_20p but with earlier saturation. This difference suggests that using multi-percentile statistics allows the model to capture temporal variations in tidal exposure, which is essential for determining elevation in dynamically wetted areas. Geographic coordinates (X,Y) reveal broad spatial gradients in predicted elevation that are further modulated by spectral variables, indicating regional-scale variations in coastal morphology captured by the model. These findings align with established coastal remote sensing understanding and confirm that the model's predictions are based on interpretable, physically meaningful features.

To validate the selection of DeltaDTM as the backshore baseline, we comprehensively evaluated available global elevation products. We excluded coarse-resolution datasets such as GLL_DTM_v2, CoastalDEM, and MERIT DEM (∼ 90 m), as their resolution is too low to capture beach micro-topography (Kulp and Strauss, 2018; Vernimmen and Hooijer, 2023; Yamazaki et al., 2017). Consequently, we focused on seven high-resolution (∼ 30 m) global products: DeltaDTM, DiluviumDEM, AW3D30, Copernicus DEM, FABDEM, NASADEM, and SRTM (ESA, 2024; Hawker et al., 2022; NASA, 2020). The assessment was rigorously conducted at both beach-unit and aggregated scales, with airborne Lidar serving as the validation benchmark. Analyses were strictly limited to the elevation range of -2 to 10 m.

Figure 13a–b show boxplots of per-beach spatial coverage and vertical accuracy (RMSE), illustrating site-to-site variability. Similarly, Fig. 13c, d provide aggregated statistics for the entire study area, giving a holistic performance overview. The results reveal a critical trade-off between coverage and accuracy. In coverage (Fig. 13a, c), conventional, gap-filled DEMs have a clear advantage: NASADEM achieves the highest coverage (58.7 %), followed by SRTMDEM (56.0 %) and AW3DDSM (53.8 %). Among coastal-corrected products, DiluviumDEM, FABDEM, and COP30DEM show similar coverage (about 47 %). Notably, DeltaDTM has the lowest overall coverage (46.9 %), reflecting its strict quality control that excludes uncertain intertidal pixels.

However, the accuracy assessment (Fig. 13b, d) shows that DeltaDTM's conservative masking yields the highest vertical reliability. Due to vegetation bias and lack of tidal corrections, general-purpose datasets (SRTMDEM, NASADEM, AW3DDSM) perform poorly, with RMSEs exceeding 2.7 m (Fig. 13d). Among the better-performing candidates, DeltaDTM achieves the highest overall accuracy (RMSE = 1.37 m). COP30DEM (1.39 m) and FABDEM (1.49 m) are close competitors but slightly less accurate. Despite its coastal design, DiluviumDEM shows a higher RMSE (1.66 m), suggesting its interpolation strategy introduces vertical uncertainty.In summary, although DeltaDTM provides the least spatial coverage, it achieves the highest vertical accuracy among all evaluated 30 m products. For our framework, minimizing baseline vertical error is prioritized over initial coverage, as systematic biases are difficult to correct. Therefore, DeltaDTM was selected as the optimal vertical reference, providing the most accurate structural foundation. The NZ-BeachTopo30 dataset supplements this foundation with the missing intertidal zones. It yields a complete dataset that outperforms all individual existing products.

As global warming intensifies, sea-level rise has become one of the most prominent climate change-induced threats to coastal ecosystems and human settlements. The Intergovernmental Panel on Climate Change (IPCC) has predicted that global sea level will rise by 40 to 90 cm by the end of the 21st century, and regional variations may lead to even higher local sea-level rises in some coastal areas (IPCC, 2023). Such changes will significantly increase the risk of coastal inundation, especially for low-elevation zones like beaches, intertidal zones and foreshores. Accurate assessment of inundation extent under sea level rise scenarios is therefore crucial for formulating scientific coastal management strategies and disaster prevention measures.

To address this need and verify the reliability of topographic datasets in inundation assessment, this study conducted a focused analysis. Using the airborne Lidar DEM as the ground truth, 335 beaches with complete Lidar coverage were selected within the study area. The inundation area under a 1 m sea-level rise scenario was calculated for three datasets including DeltaDTM, NZ-BeachTopo30, and the Lidar DEM. To simulate realistic inundation, a hydrological connectivity analysis was applied using a 4-connected neighborhood rule. First, based on the preprocessed coastline (Sect. 3.1.3), pixels with elevation ≤ 1 m were identified as initially inundable. Then, using a 4-connected rule (considering only edge-adjacent pixels), the algorithm iteratively expanded this area by adding any connected pixel also ≤ 1 m, continuing until no new pixels qualified. Finally, the inundation area was calculated by summing the areas of all inundated pixels. All datasets were projected into NZTM2000 to ensure spatial accuracy during area calculation. Based on the Lidar-derived inundation results, the inundation areas from DeltaDTM and NZ-BeachTopo30 were plotted against their corresponding Lidar values as scatter plots (Fig. 14a, b), enabling a quantitative assessment of their accuracy under sea-level-rise scenarios. Additionally, to visually compare inundation extents, spatial pattern maps were generated for two randomly selected beach units (Fig. 14c, d), highlighting the differences between DeltaDTM and NZ-BeachTopo30. Figure 14a (Lidar DEM vs. DeltaDTM) shows that the original DeltaDTM has obvious shortcomings in reflecting inundation area. Although the horizontal axis representing Lidar inundation area has a wide variation range, the vertical axis representing the corresponding inundation area from DeltaDTM is close to 0, resulting in a negative coefficient of determination (R2 = -0.092). This indicates an extremely poor linear relationship between the DeltaDTM and Lidar DEM. Statistical error metrics also show large absolute deviations, with RMSE = 0.0378 km², MAE = 0.0111 km², and a negative mean bias error (MBE = -0.0108 km²). This suggests that DeltaDTM generally underestimates inundation area, as many points cluster near zero on the vertical axis, reflecting its lack of coverage in low-elevation intertidal zones. Technically, this underestimation is due to data gaps in DeltaDTM for intertidal zones and shoals, as well as limitations in resolution and acquisition timing. As intuitively demonstrated by the scatter distributions and the newly added marginal boxplots in Fig. 14, it is evident that the baseline DeltaDTM systematically omits low-lying beach areas and regions immediately adjacent to the ocean (often returning “NoData” or severely positively biased elevations). This systematic omission highlights the limitations of traditional global DEMs in capturing the intertidal zone. In contrast, our proposed framework successfully reconstructs these missing nearshore gradients, effectively bridging the critical data gap between the ocean and the backshore. These factors prevent it from capturing actual inundable areas under low-elevation thresholds (e.g., 1 m), leading to severe underestimation of exposure under sea-level rise. In contrast, Fig. 14b (Lidar DEM vs. Predicted DEM) shows that NZ-BeachTopo30 agrees well with Lidar for inundation area estimation, with R2 = 0.894 (indicating strong agreement), RMSE = 0.0118 km², MAE = 0.0048 km², and MBE = -0.0032 km². This high correlation is largely attributable to the accurate reconstruction of low-lying pixels (≤ 1 m). As shown in Fig. 14a, the original DeltaDTM completely failed to capture these zones. Therefore, the reliable assessment of these high-risk areas is made possible solely by our gap-filling predictions. Figure 14c and d illustrate the spatial inundation patterns of two representative beach units under a 1 m sea-level rise scenario. Both subplots clearly show that the result adds numerous relatively continuous inundation zones along the shoreline and within the intertidal low-lying areas. These newly added inundation areas are adjacent to the zones identified by DeltaDTM, effectively bridging gaps in the original coverage and extending inundation mapping into previously unrepresented intertidal zones. This pattern confirms that NZ-BeachTopo30 successfully supplements near-shore lowland topography, compensating for DeltaDTM's gaps by greatly improving the mapping of terrain ≤ 1 m. This finding is fully consistent with the earlier statistical analysis. Consequently, these observations lead to two primary conclusions and several recommendations. First, from the perspective of emergency and risk assessment, the direct use of the original DeltaDTM under sea-level rise scenarios will significantly underestimate the inundated area, especially in low-elevation, sensitive zones such as intertidal zones and foreshores. Given that other open-source global or regional DEMs typically suffer from similar limitations in intertidal coverage and vertical accuracy, this issue of underestimation is likely prevalent in assessments relying on these datasets as well. Second, the XGBoost-based topographic reconstruction method proposed in this study, which integrates ICESat-2 and Sentinel-2 data, demonstrates high reliability in national-scale beach inundation assessment. It can significantly improve the accuracy of inundation area estimation, thereby providing more reliable data support for coastal management, risk assessment, and adaptation strategies such as flood zoning and ecological protection planning. It is important to highlight the following limitations: Inundation simulation relies on vertical datum and tidal level assumptions. This study uses a uniform 1 m increment relative to the EGM2008 datum, where 0 m is treated as Mean Sea Level (MSL), and does not account for local tidal levels, storm-surge superposition, or real-time tidal changes. Actual MSL often deviates from this idealized 0 m benchmark due to regional oceanographic and geodetic factors. Thus, the 1 m scenario primarily highlights the performance gap between products, rather than predicting absolute inundation. For more accurate sea-level rise inundation or erosion analysis, it is necessary to determine the precise local MSL height first and then conduct inundation simulations based on that. Additionally, for complex geomorphic areas such as extreme estuaries, tidal channels, or heavily engineered coastal segments, the model may still produce large case-specific errors. Therefore, in such areas, we recommend using high-resolution Lidar or field surveys for validation and correction, and integrating local MSL data for realistic assessments.

The method proposed in this study has strong potential for global application and scalability: the three core datasets used (ICESat-2, Sentinel-2, and DeltaDTM) are globally available, ensuring data accessibility for replication in other coastal regions. Specifically, for filling intertidal and shallow-water gaps in existing public DTMs (e.g., DeltaDTM), this method can directly enhance spatial coverage and topographic representativeness, thus offering broad applicability and practical utility.

However, the robust global application of this method faces several challenges. First, regional variations in tidal regimes can profoundly alter the spectral-elevation relationship, affecting intertidal height retrieval. Specifically, the persistent tidal biases associated with sun-synchronous sensors pose a major challenge for large-scale coastal remote sensing (Bishop-Taylor et al., 2019; Fitton et al., 2021). Our framework benefits from New Zealand's predominantly semi-diurnal tidal regime (M2 cycle of ∼ 12.4 h). Over the 5-year observation window, Sentinel-2's fixed overpass time naturally samples the complete range of tidal phases, ensuring that our multi-percentile composites genuinely reflect full tidal exposure dynamics. However, applying this statistical percentile approach to regions dominated by diurnal tides (where a fixed overpass time may repeatedly capture the same tidal phase, leading to severe tidal aliasing) will result in percentiles lacking consistent physical meaning. To mitigate this at a global scale, the temporal compositing strategy must be explicitly coupled with regional hydrodynamic models to strictly filter imagery based on absolute tidal stages rather than relying solely on observation percentiles. Additionally, implementing a regionalized modeling approach can further alleviate these spatial inconsistencies. By clustering coastal segments based on distinct tidal characteristics – such as tidal range, phase, and geomorphic type – independent, localized machine learning models can be trained to accurately capture the specific spectral-elevation relationships unique to each tidal zone. Second, the global heterogeneity in sediment properties, algal cover, and water reflectance means spectral features may not have universal topographic interpretations, complicating model transfer. Third, the non-uniform observation density and geometric distribution of ICESat-2 may leave some coastal segments with insufficient vertical control points. Fourth, the uneven global availability of high-precision validation data (e.g., airborne Lidar) hinders rigorous product assessment and error correction. Fifth, the current framework is specifically optimized for open sandy beach environments, intentionally excluding extensive muddy tidal flats and estuarine systems. This is because sandy beaches and muddy tidal flats exhibit fundamentally different spectral-elevation relationships: tidal flats typically possess much gentler gradients, distinct sediment properties (mud/silt), and higher moisture retention capacities. Extending this approach to tidal flat environments is highly feasible but would require additional feature variables, such as multi-percentile statistics of MNDWI and NDVI, as well as a regionalized modeling framework based on coastal geomorphological classification to avoid cross-domain prediction errors. More broadly, in dynamic environments like estuaries and engineered coasts, statistical models relying on spectra and sparse elevation points may struggle to capture intricate topographic details.

While our framework successfully generates national-scale beach topography, several data-product-level limitations must be acknowledged. First, the spatial extent of the modeled beaches is inherently constrained by the baseline OSM polygons. Consequently, any existing omissions or geometric inaccuracies within the crowdsourced OSM data may propagate into our final maps. Second, our dataset represents a temporally composited “mean state” generated from a 5-year observation window (2018–2023). Because sandy beaches are highly dynamic environments undergoing continuous morphological evolution, this static dataset cannot capture short-term temporal changes or extreme storm-induced morphodynamics. Third, the 30 m spatial resolution, while suitable for national- and regional-scale assessments, may be insufficient for accurately resolving the micro-topography of extremely narrow or pocket beaches. Finally, the transferability analysis (Sect. 4.4) is constrained by the uneven distribution of airborne Lidar validation data, which tends to concentrate in more accessible or higher-priority coastal segments. The performance of the model on remote, poorly accessible beaches could differ from the reported metrics, and users should be mindful of this when applying the product to such areas.

The beach topography produced in this study has substantial application potential, with one of the most significant advantages being the ability to derive reliable beach slope metrics across the entire coastal profile. Because the reconstructed elevation surface is continuous from the backshore through the intertidal zone, slope can be calculated directly from the gridded product without requiring synchronous tidal information or instantaneous water-line observations (Vos et al., 2020). This continuity avoids the discontinuities, tidal artefacts, and segmentation errors that occur when slopes are estimated from traditional datasets that lack intertidal coverage, such as DeltaDTM or single-date shoreline-based methods. As a result, the derived cross-shore and alongshore slopes more accurately represent true morphology and are suitable for sediment budget analyses, erosion susceptibility assessment, coastal hazard classification, and parametrization of morphodynamic or wave-runup models. In addition to slope estimation, the continuous elevation data also improve the computation of profile curvature, beach volume, shoreline position metrics, and baseline topography for change detection. The inclusion of newly filled low-elevation areas strengthens the reliability of inundation and flood-risk modeling by reducing systematic underestimation of low-lying terrain. Furthermore, the dataset provides a consistent and vertically harmonized terrain reference that can be integrated into coastal planning, environmental management, emergency response, and calibration of local high-resolution surveys, offering a more robust foundation for national-scale coastal analyses.

To increase temporal fidelity, spatial resolution, and operational readiness, several technical developments should be pursued. First, static ancillary layers derived from OSM should be replaced or supplemented by time-resolved land cover and shoreline products based on Sentinel-2 time series, for example Google's Dynamic World and other Sentinel-2 LULC maps, which enable the definition of temporally varying beach extents and improve discrimination between transient tidal inundation and persistent surface types (Brown et al., 2022). Second, improving spatial granularity is achievable by leveraging the native 10 m Sentinel-2 bands together with denser sampling strategies for ICESat-2 control points or multiyear retracking approaches; this could support seasonal or annual 10 m reconstructions provided that co-registration, along-track footprint geometry, and sample density are carefully addressed and that targeted UAV or airborne Lidar surveys are used for local calibration and validation. Third, advanced modeling architectures and uncertainty aware frameworks merit exploration, because convolutional and attention based deep networks, graph neural networks, and physics informed models can better exploit spatial context and incorporate physical constraints, while ensemble, Bayesian, or Monte Carlo approaches can quantify predictive uncertainty to support probabilistic risk assessments. Fourth, feature engineering should be extended beyond single percentile predictors; multi percentile statistics such as p20, p50, and p80 of NDWI and NDVI, and percentile difference metrics such as NDWI p80 minus p20, encode exposure and tidal occurrence and can substantially improve prediction of intertidal elevation, and temporal trend indicators, texture measures, and SAR derived wetness or backscatter provide complementary information in cloudy or turbid conditions and should be evaluated systematically. Integrating these advancements will be key to achieving high-frequency, global-scale coastal monitoring with enhanced precision and operational readiness.