In a PLS setup, a TLS is permanently mounted and acquires elevation data as point clouds over regular intervals for an extended period of time. For this study, a dataset of 21 780 hourly point clouds is used, acquired with a Riegl VZ2000 at Noordwijk, the Netherlands (Fig. ) between 11 July 2019 and 21 July 2022 . The scanner was positioned on a hotel at 55.575 m above Normaal Amsterdams Peil (approximate Mean Sea Level in the Netherlands, MSL). Figure  shows a coloured version of one point cloud in the time series. Elevation measurements of the dune area, backshore, and part of the intertidal area are obtained. Spatial gaps in the data exist because of occlusion from the single viewpoint of the permanent TLS position. Consequently, the dune foot cannot be observed in the data. Details on the data characteristics (e.g., point density and accuracy) and setup can be found in .

Several pre-processing steps are undertaken before surface dynamics are extracted from the point cloud time series. First, the XYZ values of each point cloud are corrected for scanner tilt using transformation matrices as provided with the dataset at 4TU.research data . This reduces the systematic error between consecutive point clouds due to, for example, heat effects and storm conditions . There are some temporal gaps in the dataset of which the longest is 1.5 months. These occur due to system failure, periods of bad weather, or maintenance. Some point clouds in the dataset were found to be noisy, containing points over the whole field of view, mostly below the actual topography. These point clouds are removed by filtering based on thresholding of the lowest 10th percentile of the z-value of the point clouds. If this is lower than -60 m in the local coordinate system established by the scanner position, thus corresponding to -4.425 m a.m.s.l., the point cloud is not used. Finally, the remaining 21 194 point clouds are cropped to contain only the area indicated in Fig. . The dune area is cropped out, as the vegetation obscures most of the sand transport. The far intertidal area is not used as only little data is available from this area, because the near-infrared LiDAR does not penetrate water .

The environmental dynamics considered in this study are obtained from hydrodynamic and meteorological measurements. Their relation to surface dynamics is assessed through several parameters representative of wave, water level and wind dynamics, namely, the significant wave height (Hs), period of significant waves (Tp), the water level (Wh), mean wind speed (u), and the wind direction (θ). These dynamics are chosen as they are input variables in most hydro- and morpho- dynamic models . Other possibly important variables like wave direction, precipitation or socioeconomic factors like the crowdedness are not considered in this study, but could be added in future work.

For the analysis the wind direction is converted to the direction in degrees with 0° in along shore direction (θcoast). The sine of the angle then gives a continuous variable with 1 being seaward wind direction, 0 for wind parallel to the coast (in both directions), and -1 for landward wind.

The meteorological dynamics are obtained at an hourly interval at Hoek van Holland by the Dutch Meteorological Institute . The hydrodynamics are also provided hourly. The parameters related to wave dynamics are measured at IJmuiden and the water level at Scheveningen. Both by the Public Works and Water Management Department of the Netherlands . They match the acquisition time of each point cloud. Locations of the different measurements stations are visualised in Fig. . The monitoring stations are located at distances up to ∼ 35 km from the PLS site. Meteorological and hydrodynamic conditions along this stretch of the Dutch North Sea coast are, however, highly spatially coherent at the timescales considered in this study. Wind speed over the southern North Sea has a decorrelation length on the order of hundreds of kilometres for daily variability , with Hoek van Holland and IJmuiden showing similar wind statistics . Wave conditions along the Dutch coast are also spatially homogeneous, with observed deviations in mean significant wave height on the order of only 0.2 m .

From the point cloud time series of a permanent laser scanner, surface dynamics as 4D-OBCs are extracted. A 4D-OBC represents a spatiotemporally confined surface dynamic event like the deposition and consecutive erosion or transport of an intertidal bar. In other words, it is an elevation change defined through a fixed timespan and with a fixed planimetric extent. These temporary surface dynamics are extracted through the 4D-OBCs algorithm, as available in the py4dgeo Python software . This algorithm consists of several steps, to extract a set of spatiotemporal segments (4D-OBCs) from a point cloud time series, which we explain in the context of the analysis of the work in .

The extraction of the 4D-OBCs potentially results in a set of thousands of spatiotemporal objects representing the extent of single unordered temporary surface dynamics. The 4D-OBCs need to be further processed and characterized, to be able to group them into different types and identify recurrent 4D-OBCs. Processing of the 4D-OBCs is done by filtering the set of extracted 4D-OBCs, merging 4D-OBCs with large spatiotemporal overlap, and extracting internal features that describe the remaining 4D-OBCs.

The set of 4D-OBCs is clustered based on the previously extracted internal features to obtain distinct groups of dynamics of which the characteristics can be analysed. This is done in three steps to allow for the analysis of surface dynamics of different levels of detail, e.g., low-level analysis of intertidal vs. backshore dynamics, and high-level analysis of different types of backshore dynamics. The dataset is first split into erosional and depositional 4D-OBCs, based on the sign of the seed elevation time series of each 4D-OBC. These depositional 4D-OBCs are thus characterised by an initial increase in elevation, and a consecutive decrease, i.e., temporary deposits; vice versa for the erosional 4D-OBCs. In the rest of this paper we refer to them as depositional or erosional objects, respectively, even though they both contain a depositional and an erosional component. The second step projects the 4D-OBCs into a detailed 2-dimensional lattice using a Self-organizing Map SOM;, following the approach by . The third step then clusters the nodes of this lattice at different hierarchy levels using hierarchical clustering. This combination of methods provides a balance between overfitting on outliers and overfitting on frequent dynamics.

SOMs are chosen because they provide a largely topology-preserving projection of high-dimensional data onto a 2D lattice, making inter-sample similarity visually inspectable without requiring a prior definition of the number of clusters. This is particularly suited to our dataset where surface dynamics form a continuum of types depending on research focus rather than discrete natural classes. Hierarchical clustering is subsequently applied to SOM nodes because it allows cluster boundaries to be explored at multiple levels, which makes them especially useful in the scale-dependent coastal setting, where different research questions call for different levels of morphodynamic detail to be explored.

The conditions and temporal patterns of the surface dynamics in the identified clusters are analysed using the active count time series of 4D-OBCs per cluster. The active count at a given epoch is defined as the number of 4D-OBCs that have started before that epoch but have not yet completed. By computing this separately per cluster, we can compare the temporal activity of different surface dynamic types. The active count serves as a proxy for process energy: a higher count implies that more sand transport events of that type are simultaneously ongoing, which can be related to the prevailing environmental conditions. It does not, however, quantify the absolute volume of sand transported, which would require integration of the volumeTS across all active 4D-OBCs.

To evaluate the applicability of the workflow for the extraction and grouping of short-term surface dynamics occurring at different moments in time, the output of Step 3 of the workflow (Sect. ) is evaluated in two ways. We investigate the feature distributions of a selection of the obtained clusters and assess their separation and coherence manually, and using the silhouette score (Ssil, Eq. ). Furthermore, for one of the clusters the set of 4D-OBCs grouped in the cluster are investigated manually, to benchmark if these indeed appear similar, and can be interpreted as a similar type of surface dynamics. A single cluster that represents berm deposition is selected for this detailed illustration, because berm deposition is one of the most recognisable morphodynamic processes at the study site, providing a clear basis to evaluate whether the grouped 4D-OBCs represent similar type of events. Finally, we assess the variation in the appearance of different groups of surface dynamics, by computing their relative frequency per season. This is computed as the fraction of 4D-OBCs assigned to a given SOM node that were initiated during a particular season, normalised by the total number of 4D-OBCs initiated in that node across all seasons. In practice, the spatial characteristics and time series of multiple clusters were inspected by the authors to assess physical coherence; these broader checks inform the interpretation of all eight clusters presented in the results.

To assess the usefulness of the workflow for linking activity of different surface dynamics to environmental dynamics, the active count time series (Step 4, Sect. ) is assessed. We notably investigate the changes in activity of a set of clusters in relation to a particular sequence of environmental conditions, here in winter 2019/2020. We focus on identifying whether variations in the activity of different groups can be related to known physical processes that lead to sand transport on beaches. We investigate to what extent certain thresholds in wave height, and extended phases of specific wave conditions, like increased wave period, can trigger changes in activity of intertidal and lower backshore dynamics; and if certain variations of wind speed and direction lead to triggering of specific activity of surface dynamics present on the backshore. Finding and interpreting such triggers and conditions within established conceptual models would indicate that the grouping is indeed physically valid, and could be used for obtaining specific insight in the conditions of selected types of surface dynamics.

The initial grouping using a Self-organizing Map (SOM) results in two lattices, one for erosional (E-SOM, Fig. a) and one for the depositional 4D-OBCs (D-SOM, Fig. b) that present the distribution of features (Table ) among the dataset. We create lattices of 8 by 8 nodes, thus 64 nodes in total, that are hexagonally linked. Figure a and b show the distribution of the cross-shore location and volume change time series shape for, respectively, the depositional and erosional 4D-OBCs in the dataset.

Through the SOM we can identify how these features vary over the set of 4D-OBCs, and thus present characteristics of the different surface dynamics they represent. The cross-shore location showcases a great ability to distinguish the 4D-OBCs into a global feature variation. Clearly, the erosional and depositional 4D-OBCs can be distinguished by their location in the intertidal area, berm, or backshore. Additionally, one can identify that the area of the SOM describing backshore 4D-OBCs is smaller for the erosional dynamics (nodes of column A–H, row 8, in Fig. a) than for the depositional dynamics (nodes of column A–H, row 1–4 in Fig. b). This can imply two things, namely, the diversity in the erosional dataset in terms of the applied features is less, or the erosional set of 4D-OBCs is more dominated by intertidal and berm activities than the depositional set.

On a local scale, so both in intertidal, berm and backshore locations, a sorting can be identified based on the slope of the growth and decay phase of 4D-OBCs. For example, the D-SOM showcases a set of abrupt 4D-OBCs on the far landward beach (e.g., nodes C1 and D1), whereas slightly more seaward on the berm, more nodes with gradual growth of 4D-OBCs are visible (e.g., nodes F5 and G5). This variation in slope of the deposition might be linked to variations in underlying processes driving the dynamics. These maps thus allow us to investigate distributions of features and shapes of dynamics captured by the 4D-OBCs.

Some nodes are very similar, and only differ slightly in, for example, their time series shape (compare Fig. a node A1 and B1). As such, to go beyond the study of global feature distributions of dynamics, and further study particular types of dynamics like e.g., berm deposits or bulldozer effects, further grouping of these detailed nodes is required. The SOM nodes are grouped using hierarchical clustering (Sect. ), with a distance threshold of 0.26, and 0.3, for the erosional and depositional SOMs, respectively. This leads to silhouette scores of 0.23 and 0.24, following Sect. . For each SOM (Fig. ), the colour of the outline of a node indicates a separate cluster. Similar colours in Fig. a and b do not imply similarity between erosional and depositional clusters, they are independent. A Principal Component Analysis (PCA) projection of the 4D-OBC feature space and SOM node positions is provided in Appendix A (Figs.  and ), illustrating the distribution of 4D-OBCs and SOM nodes across the two principal dimensions of feature variation for depositional and erosional dynamics, respectively. Dendrograms of the hierarchical clustering are also provided in Appendix A (Figs.  and ), showing the distances at which SOM nodes are merged and the relative separation of the identified clusters.

From the 2 × 64 SOM nodes, 14 depositional and 17 erosional clusters are identified. From each of these sets, we further investigate four selected clusters, which are interpreted based on their feature characteristics. Figures  and , display the distribution of five selected features for these eight clusters. The colours correspond to the colours in the respective SOM. The four erosional clusters show a clear separation based on their cross-shore location (crossLoc) and magnitude, and can thus be interpreted as far and deep intertidal (cluster E8), shallow intertidal (cluster E7), and two types of backshore erosion with different magnitudes (cluster E2 and 0). The far and shallow intertidal erosion clusters are comparable in their duration, which is on average shorter than two weeks (Fig. b). However, they are well distinguishable by their difference in area, magnitude, and and minimum slope (minSlope, Fig. c, d and e). Namely the far intertidal dynamics are smaller in area, potentially due to more gaps in the data, and have a lower magnitude minSlope, they thus grow deeper, faster. The two types of backshore erosion cover very similar cross-shore locations, but can also be distinguished by their area, magnitude and minSlope. Namely, cluster E0 contains larger erosional dynamics (> 1000 m²), that can grow deeper over a shorter period of time than cluster D1 (Fig. c, d and e). More specifically, cluster E0 describes erosional dynamics that can cover the full beach width in size.

The four depositional clusters also display this clear separation based on their crossLoc and magnitude (Fig. a and d), and can thus be interpreted as large intertidal bar deposition (cluster D11), berm deposition (cluster D4), and high magnitude (cluster D7) and low magnitude far backshore deposition (cluster D1). Further characterisation is done based on the duration, area and maximum slope (maxSlope, Fig. b, c and e). The intertidal bar depositions are only of a large area (around 1000 or more m²), and have a longer duration than the berm depositions (several weeks compared to one week). Figure c, shows an example of one of the intertidal bars of cluster D11, whereas Fig. b shows a large scale berm deposition of cluster D4. The latter can be interpreted as the gradual welding of a bar to the berm. The two backshore clusters are easily distinguishable by their magnitude and maxSlope, with cluster D7 being a lot higher in these regards. This high magnitude, and maxSlope might indicate dynamics that are of human origin. If we inspect the outline and time series of volume change of one of the 4D-OBCs found in this cluster (Fig. a), it can be seen that it is a very local change, and surrounded by areas of erosion of comparable magnitude. This suggests local sand transport by bulldozers. The large spread in duration of the 4D-OBCs in this cluster also suggests that the changes they describe are not of a nature that is easily adjusted for in a natural morphodynamic equilibrium.

Following the extraction and interpretation of different types of short-term surface dynamics based on the internal characteristics of the 4D-OBCs, we can now investigate if and how these groups exhibit variation in their temporal occurrence over the years. Figures  and display the relative occurrence of 4D-OBCs in different SOM nodes (Sect. ) in the four seasons computed over the three-year dataset.

Figure  clearly shows varying activity of different types of dynamics in different seasons. In winter, 4D-OBCs occur over the whole SOM space with few exceptions, whereas in spring only relatively few 4D-OBC are active. In summer and autumn, the activity is unevenly distributed. In summer, the erosional dynamics that occur are found mainly at the bottom of the SOM. These nodes correspond to 4D-OBCs on the backshore (Fig. d). In autumn, on the other hand, the active nodes are mainly at the top right of the SOM, corresponding to 4D-OBCs located in the intertidal zone. However, other nodes representing intertidal surface dynamics are not as active (lower left of the SOM). This indicates that different types of intertidal dynamics are active in different seasons.

Figure  displays a comparable pattern of seasonal variations, where the main difference is the lack of depositional activity in the top right of the SOM in winter. This corresponds to the area of the SOM with 4D-OBCs of the backshore (Fig. b). Thus, little deposition on the backshore takes place in the winter. Whereas in summer most of the backshore depositional dynamics occur, and only relatively little intertidal depositional 4D-OBCs (lower left in Fig. b).

These results show that particular seasons are dominated by both erosional and depositional surface dynamics. This indicates that in these seasons erosional and depositional dynamics coexist in different parts of the beach, or that they appear in periodic sequences throughout a season. Further investigation of a sequence of surface dynamics activity might demonstrate this.

To further demonstrate the applicability of the workflow for studying characteristics of short-term surface dynamics, we compare the variation in active count time series of the eight interpreted clusters (Sect. ) to variations in environmental variables, as described in Sect. . We do this on a detailed scale by zooming in on a five month period of activity in the selected clusters between November 2019 and April 2020 (Fig. ).

In the top five panels the environmental dynamics are plotted. Here we take the 24 h rolling mean for better interpretability. Figure A, B, C, D, and E display the sine of the wind direction (Sect. ), wind speed, significant wave height, wave period, and water level, respectively.

The extraction of surface dynamics as 4D-OBCs enable the analysis of spatiotemporally coherent segments of elevation change. In previous work, these have been extracted and validated for datasets of 4D topographic measurements up to several months with around 3000 hourly epochs . In the workflow presented here we enable the extraction of 4D-OBCs from even longer time series of hourly point clouds, where computational memory and time-constraints limit applicability, by enabling parallel computation in subsets, and serial computation in seed batches. In combination with the application of the C++ implementation of the 4D-OBC algorithm in the open-source Python library py4dgeo , we achieved extraction of 4D-OBCs and derivation of features from a set of 21 194 point clouds in only 18 h on an HPC (48 cores, 2 × Intel Xeon E5-6248R, 3.0 GHz, and 768 GB RAM), with subsequent clustering on a relatively small workstation within 1 h (32 GB RAM, 24 cores). This efficient processing offers the potential to further apply the methods on even larger datasets in future work, with the possibility of incorporating 4D-OBC detection on hierarchical spatiotemporal scales.

The application of the SOM on the extracted 4D-OBCs enables the unsupervised grouping of the full set of 4412 4D-OBCs based on the internal distributions of eight derived features, such as duration, cross-shore location, and magnitude of elevation change. The SOMs capture non-linear patterns in the eight-dimensional feature space and offer an intuitive layout for assessing inter-node similarities. Visualising a feature like volume time series shape, along with cross-shore location, enables the identification of patterns of characteristics in the dataset of surface dynamics. For example, the erosional dynamics show a lower diversity in or number of backshore dynamics than the depositional dynamics, indicated by the smaller apparent area of backshore dynamics in the respective SOM (Fig. a).

Through hierarchical clustering of SOM nodes, we identify 14 depositional and 17 erosional dynamic types. The clusters have coherence in their internal features and allow for interpretation of morphodynamic processes such as berm deposition, large-scale beach erosion, and anthropogenic activity. For example, cluster D7 can be linked to localized sand placement, likely by bulldozers, based on its high magnitude, rapid volume change, and spatial characteristics that are different to natural deposition patterns. This opens up the possibilities to study relative impacts and frequencies of anthropogenic dynamics, which have been previously found in these datasets , but to the best of our knowledge not studied in detail.

These findings highlight how unsupervised clustering methods applied to the 4D-OBC feature space can, for this environmental setting, extract morphodynamically meaningful patterns without the need for predefined class labels or thresholds. Which is demonstrated for the eight clusters investigated in this study. The clustering method greatly advances existent methods of PLS data analysis , as we are now able to bring together similar 4D-OBCs, i.e. instances of surface dynamics types, occurring at different moments in time. Consequently, this enables us to study the different environmental conditions, or periods in which surface dynamics with different characteristics exist. Moreover, the grouping allows for identifying variations in location of morphodynamic zones, given by temporal cross-shore location patterns in the occurrence of specific types of dynamics. These zonations can reflect patterns of change in the extent to which hydrodynamic or meteorological forces can affect sand transport in the beach system and can thus provide a new way of analysing changes in drivers of cross-shore dynamic zonation.

The SOM provides a scalable and flexible grouping method: larger SOMs could be applied to explore more complex systems or longer datasets, with hierarchical clustering acting as a second-stage simplification step. This hierarchical structure of clustering gives a high grade of visual interpretability, and allows to identify levels of grouping which, depending on the application, can be investigated at varying hierarchies (cf. the dendrogram in Appendix ). Future work could further explore and optimize the specific settings of the SOMs and clustering. We found that, with current parameters, the E-SOM shows less diversity in the identified surface dynamics than the D-SOM (cf. Appendix ), which could be due to the erosional dynamics being more consistent over time, or their variation might be in different features than for the D-SOM. Optimizing settings for the two datasets separately instead (e.g., a smaller SOM and testing spatial shape features for erosional dynamics) might increase the representativeness of the clusters.

Future clustering applications may benefit from using density-based alternatives to hierarchical clustering such as Hierarchical Density-Based Spatial Clustering of Applications with Noise , which can identify clusters of varying density and flag low-density nodes as noise. This would reduce overfitting to some outlying dynamics/artefacts by not forcing them into a cluster, as occurs in our workflow. Such methods would however require alternative validation metrics suited to density-based clustering, such as the Density-Based Clustering Validation score DBCV;, instead of the silhouette score used here. Other simpler methods like k-means clustering offer another alternative but requires the number of clusters to be predefined and assumes approximately spherical, equal-variance clusters, assumptions unlikely to hold for the complex varying dynamics found here.

The application of this unsupervised classification workflow is not limited to coastal areas or specifically to 4D-OBCs. The approach is generalizable to any set of time series segments of topographic measurements, enabling the identification of similarly behaving surface dynamics at different moments in time. Adaptation may be required through additional feature engineering. For instance, in a coastal setting with lower point density data such as ICEsat line-sampled measurements , temporal segments of uniform change could be identified using the breakpoint detection method (Sect. ) or trend fitting . Features could then be extracted directly from these segments, without relying on the spatial or spatiotemporal features provided by 4D-OBC region growing. Instead, additional temporal descriptors (e.g., acceleration of elevation change) could be incorporated before applying the SOM and hierarchical clustering to group locations with similar dynamics.

In other environments, such as landslide- or avalanche-prone alpine regions e.g.,, the workflow could be adapted by modifying the seed detection step of the 4D-OBC method e.g., restricting to uni-directional changes as in. Feature design and selection would also differ, e.g., slope or acceleration of elevation change could help distinguish slow mass movements from rapid landsliding, while location-based features such as the cross-shore location used in the coastal setting would be less relevant.

The temporal activity of specific clusters and SOM nodes reveals known links between surface dynamics, seasonality and environmental dynamics, including wind direction, wind speed, wave height, wave period, and tidal water levels. Seasonal patterns are present in the SOM grouping, with an increase in intertidal erosion in autumn and winter, consistent with seasonal storm-driven dynamics of sandbars . We can however identify specific types of intertidal erosion dynamics that are less active in autumn. Activity in both erosional and depositional clusters of intertidal dynamics coincided with wave heights exceeding 2 m and peak wave periods above 6 s, supporting previous findings on energetic thresholds for enabling changes in morphodynamic states of the beach . Further statistical analysis could then allow for the acquisition of site or time-specific threshold conditions in which different dynamics take place.

Through investigation of the relative activity, we show that wind speed and direction, in combination with fetch and obstructions, have a complicated but strong relation to patterns of activity in backshore depositional and erosional dynamics. Small scale erosional clusters gain an increase in activity under shorter fetch conditions through a seaward wind direction, which respond most sensitively to sustained high wind speeds (> 10 m s⁻¹). In contrast, small depositional clusters on the far backshore get activated under similar windspeed, when there is an alongshore direction. Their deposition is likely the result of obstruction by buildings, creating local turbulence and lowering of wind speed. These findings support earlier research highlighting the complex interaction between fetch length, and threshold wind velocity for aeolian transport initiation and deposition , and emphasize the need for considering (man-made) obstruction when predicting sand transport processes .

In addition to peak event characteristics, the duration of high-energy wave conditions also influences morphodynamic response captured in the 4D-OBCs. Extended periods of elevated wave energy and water level lead to increase in intertidal erosion clusters. Moreover, variations in berm deposition can be related to sustained variations in wave period and wave height, whereas short peaks do not seem to have a similar effect on activity of berm depositions. These observations are in line with the concept of morphological relaxation time, varying periods of energetic conditions are required to drive substantial adjustments in intertidal bar systems of different scales .

Future studies could include more environmental dynamics, such as wind speed variance, wave direction, precipitation, and combined multivariate dynamics, e.g., through principal component analysis or multivariate time series analysis. Moreover, quantification of thresholds for the initiation of different dynamic types, or even a statistical or causal analysis of interactions between environmental dynamics and surface dynamics could inform a data-driven way of modelling of short-term surface dynamics processes.

In particular, the found groups of surface dynamics, together with these environmental dynamics can be used to develop physics-based prediction models of surface dynamics that could inform coastal management. By combining observed surface dynamics and time series of environmental variables, physics informed machine learning methods could learn specific conditions linked to surface process activity, which in this study were identified manually. Through these predictive models one might then anticipate certain high-impact dynamics and possibly prepare through adequate beach management. Additionally, these short-term prediction models could be extrapolated to future climate scenarios to identify possible impact on longer-term morphodynamic projections.

The interpretation of the results highlights the inherent complexity of the coastal system. Even under seemingly similar environmental conditions, the temporal patterns in activity across clusters of surface dynamics vary considerably, suggesting that there are other, possibly unmeasured, factors influencing the response. This includes the sequence of events, the previous morphological state, sediment availability outside of the measured area, or other cumulative effects. It furthermore emphasizes self-organization in the system, as the current state affects how the system evolves, even without a clear or direct external trigger . Sediment availability from along-shore transport or the foreshore are not directly measured as potential environmental drivers in our study but assumed to be implicitly reflected in the extracted 4D-OBCs and history of environmental variables. In a future PLS setup, explicit monitoring of these boundary conditions (through e.g., regular monitoring with bathymetric sensors, wider-area UAV surveying, or acoustic sediment transport sensors), or exploration of the prediction thereof through the history of environmental variables in combination with, for example, LSTMs, could aid further explanation of identified beach dynamics and their variation.

Nonetheless, the results show that the characteristics of the grouped 4D-OBC clusters, and their temporal variations, are interpretable in terms of known coastal processes. What this method offers is not a complete explanation of morphodynamics in a PLS dataset, but rather a structured way of reducing the high dimensionality of extensive point cloud time series into types of surface dynamics. This discretization enables systematic comparisons, temporal analyses, and correlation studies, which would be otherwise infeasible. It also allows the targeted investigation of particular types of dynamics (e.g., berm growth, bar migration), and opens the door for more detailed analyses of their environmental drivers.

However, several methodological limitations remain. The current 4D-OBC definition is tied to temporary elevation change, but in practice, some dynamics have a net change (i.e., volume gain or loss, e.g., Fig. a node 2F). This may result from the inclusion of growing regions with only partial similarity during part of the dynamic, leading to incomplete closure of the object. As we cluster on these volume features, these types of 4D-OBCs can be distinguished afterward, and thus separately analysed and regarded. However, it is a particularity of the 4D-OBCs that does influence its applicability on studies of volume change. One possible refinement would be to define unidirectional or partial dynamics (e.g., only build-up or erosion) like previous methods . Spatially splitting objects into separate positive or negative parts might support this, e.g., by filtering individual 4D-OBCs at their spatial margins after or during region growing through testing whether added corepoints show a coherent direction of elevation change.

The current 4D-OBC filtering step, that excludes non-natural intertidal dynamics of excessive change, may in other locations exclude large but natural 4D-OBCs like sandbars under nourishments. A larger threshold may offer a better balance, but it increases the risk of outlier inclusion. Possibly, to fully avoid this step and reduce the number of outlying 4D-OBCs in the intertidal area, the point cloud time series processing could be improved upon by adding a step to filter out water points, and/or use only low-tide scans.

The choice of features influences clustering outcome, and correlated features may bias groupings. In this work the features are selected based on previous knowledge about the processes to be clustered. A data-driven feature selection, using e.g., Shapley values and a labelled dataset might increase effectiveness of the clustering. Furthermore, the way the volume time series (volumeTS, Table ) is incorporated as a feature could be changed. Currently, we resample the time series such that they all have the same number of dimensions and a Manhattan distance can thus be computed between different 4D-OBCs. In the future the use of DTW distance instead of Manhattan distance could allow to compare the time series of different lengths directly. Or, the derivation of other time series-based features alike could be used as a substitute.

The interpretation using the active count of 4D-OBCs allows us to identify the distribution of the energy of the system into different dynamics. This offers the possibility to study its variations over time and gives indications on sand redistributions over the study area. There are, however, several limitations to the extent to which these interpretations are valid. First, the active count is decreased at the start of a subset (Sect. ), and decreases per definition when coming to the end of a subset, as fewer seeds complete their deposition-erosion cycle before the subset is ended. This decreases the interpretability of changes at the margins of a subset, which should be taken into account during analysis, in particular when statistical analysis are carried out. To add continuity across subsets and reduce edge effects, future work could use only daily low-tide scans to reduce the number of epochs, and allow single batch processing, or develop a mechanism to transfer non-concluded seeds across subsets.

Furthermore, the use of a time series of volume within 4D-OBCs of different types of dynamics, instead of an active count time series could in future work be investigated. As this would actually quantify sand redistribution on the beach, and would thus be preferable for analysing sand redistribution through different surface dynamics. However, the current design of te 4D-OBC segmentation method does not allow for this. As follows from the results (e.g., object vi in Fig. ), not all 4D-OBCs fully delineate the extent of a surface dynamic, either because a surface dynamic lies partially outside of the data coverage, or because the outer areas of the surface dynamic are too different from the internal area of the seed. If a correct measure of volume inside types of dynamics is wanted, these partial 4D-OBCs should be detected and flagged, or their growth must be optimised. Additionally, for these volumetric redistribution studies the addition of the dunefoot, dune and subtidal area in the topographical data would be preferred. This would require either a higher position of the LiDAR sensor, to diminish occlusion, or the incorporation of additional LiDAR sensors targeting the dunefoot. Incorporating sand redistribution in the dune area would also require effective separation of vegetation and sand through point-wise classification methods.

The reliance on unsupervised clustering avoids the need to predefine surface dynamic classes, which is an important advantage in a natural coastal system where class boundaries are continuous and scale-dependent. This, however, means we require manual validation, and there is no quantified external validation against labelled ground truth. This makes it difficult to assess whether a given parameterisation is optimal or to compare methods extensively. In future work, development of benchmark datasets of labelled 4D-OBCs, derived using video imagery or expert annotation of known events, could enable quantitative validation, data-driven feature selection, and consequently greater confidence in the transferability of the workflow to new sites.

A limitation of the environmental analysis is the use of monitoring stations located up to 35 km from the PLS site. While the large-scale spatial coherence of wind and wave conditions along this coast justifies this for our scale of analysis, local effects and subdaily temporal variations will not be fully captured. For future data-driven correlation and prediction studies, locally measured or spatially interpolated/downscaled environmental variables would be worth investigating.