As an inherent part of regional morphometric analyses, different freely available digital elevation models (DEMs) were tested to identify the most accurate digital representation of the Skeleton Coast. The accuracy assessments were conducted for the 30 m products of the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER; Abrams et al., 2020), Shuttle Radar Topography Mission (SRTM; Farr et al., 2007), Advanced Land Observing Satellite (ALOS; Tadono et al., 2014), and the Copernicus DEM (GLO-30; Rizzoli et al., 2017). For the assessment, an approach outlined by Kramm and Hoffmeister (2019) was followed, testing the vertical accuracy against laser altimetry ICESat-2 (Ice, Cloud, and Elevation Satellite 2; Neumann et al., 2019) data. The GLO-30 product showed the best vertical accuracies (RMSE ≈ 1 m) and was therefore selected as the elevation source for morphometric analyses and fan delineation (see Appendix A for details). As an additional morphometric parameter describing surface roughness, C-band Synthetic Aperture Radar (SAR) backscatter data was acquired for the fan areas using Google Earth Engine and Sentinel-1 (S1) time series data (see Ullmann and Stauch, 2020 for a detailed method description). Sentinel-1 backscatter data has, e.g., been investigated in the hyperarid Atacama Desert, linking surface cover and surface dynamics to alterations in the backscatter signal (Ullmann et al., 2019). The backscatter signal largely relates to surface roughness and conductivity on cm-scales (e.g. Gupta, 2018); Ullmann et al. (2019) generally found a very high signal stability of C-Band in vast parts of the desert. For our study region, the S1 data available at the time of processing in Google Earth Engine was limited to the years 2017–2021, ascending orbit, and narrow incidence angle range (31.1–39.5°; collection snippet: ee.ImageCollection(”COPERNICUS/S1_GRD”)).

Co-polarised (VV) dry season (i.e., austral winter) data was averaged into a single raster at 10 m horizontal resolution, providing a noise-removed, radiometrically calibrated, and terrain-corrected product (based on SRTM DEM). Image coverage per year and pixel was consistent at 15 ± 5 images across all alluvial landforms. Such time-integrated averaging reduces speckle and minimises short-term moisture variability, producing a stable VV signal, with less alteration from individual events such as exceptional overland flow. From comparing the VV backscatter data with visual ground truthing conducted on site (e.g., Messum, Koigab; Fig. 1), we find that CaSO₄-encrusted surfaces increase signal reflectivity as compared to the non-encrusted surroundings, providing a tool for relative comparison of surface abundances indicated by the degree of encrustation (cf. Stollhofen et al., 2014).

Climate data used in this study was obtained from two sources. Firstly, satellite-derived fog and low cloud cover data for the time period 2015–2017 generated by Andersen and Cermak (2018) was provided in raw format by the authors of the original publication. The original point data (3.2 km spacing) was rasterised by ordinary Kriging using exponential semi-variogram model and variable search radius (cf. Earls and Dixon, 2007) producing a raster of 5 km horizontal resolution. To be able to calculate averaged fog occurrences over narrow landforms, the raster was resampled to 321 m resolution (nearest resampling; factor 15). Likewise, precipitation (mean annual and mean maximum) and wind speed (mean maximum) data as obtained from the CHELSA-BIOCLIM+ dataset for the time period 1981–2010 (Brun et al., 2022a, b; Karger et al., 2017) was resampled to a horizontal resolution of 303 m (factor 3).

Finally, digital geological data (lithology and faults) at a scale of 1:250000 was provided by the Geological Survey of Namibia (GSN, 1996; 1998; 2002b, a; 2006a, b; 2008; 2009; 2010b, a; 2011a, b), which we merged and broadly reclassified by rock type (sedimentary, metamorphic, and igneous subdivided into volcanic and plutonic).

Along the Skeleton Coast, alluvial deposits were mapped at the catchments' outlets, assigning one alluvial landform to a source area. This mapping strategy constitutes an oversimplification, since morphologically well-defined single fans are uncommon along the Skeleton Coast. However, it also reflects the heterogeneous nature of alluvial deposition within the study area. In general, the maximum alluvial landform extent, which could – at a high confidence – be attributed to the landform, was mapped. Especially at the apex areas, some generalization was unavoidable since the modern catchment outlet does not necessarily reflect the true palaeoapex of the alluvial landform system. The mapping of the fans belonging to the IDs #43 and #44 (Koigab) was partially based on those by Krapf et al. (2005). Outcropping bedrock was excluded from the alluvial landform polygons. Only those fans were mapped with associated catchments draining a total area larger than 4 km². Mapping was conducted using ESRI's World Imagery (true colour composites) with a spatial resolution of ≤ 0.5 m and accuracies of < 9 m. The date range and satellite types included in the composites spanned July 2018 to March 2023 and WorldView-2, WorldView-3, and GeoEye-1 (all Maxar Technologies), respectively. Aided by GLO-30-derived hillshade data, mapping was conducted in ArcGIS Pro (ver. 3.0.0) at a scale range of 1:1000 to 1:5000. The dataset includes single alluvial fans, fans as part of a bajada, fan complexes, and polygenetic fans (see Table 1 for classification by type and location). The distinction between fan complexes and bajadas generally followed the approach used by Walk et al. (2020), using 5–7 neighbouring fans as the threshold between the two groups. Polygenetic alluvial landforms are characterised by more than one major feeder channel. Mapping included parts of the sedimentary Gui-uin flood basin of the Hoanib river (e.g. Eitel et al., 2005; Stanistreet and Stollhofen, 2002), reflecting the damming situation east of the Skeleton Coast Erg as evident for most of the other adjacent systems, where the ponding is however less permanent. Given this heterogeneity in mapped alluvial deposits, we generally use the term “alluvial landform” in the main text, but use the term “fan” interchangeably, e.g., in variable notation. We justify this inaccuracy with enhanced readability and the fact that the methodological approach we chose largely excludes non-fan type landforms (Sect. 4.2).

A mapping quality assessment was performed using a four-grading system, subjectively evaluating mapping success by assigning alluvial landforms into distinct classes (Table B1). Single dunes or sand sheets covering clearly identifiable fan surfaces (i.e., not below the main body of the Skeleton Coast Erg) were not clipped out, as they represent temporary (on very short timescales as compared to the erg) morphodynamic features.

Upstream of the apices, the corresponding catchments were identified by watershed delineation in ArcGIS Pro (ver. 3.0.0) using the GLO-30 DEM. In order to obtain an optimised delineation result ignoring effects of DEM artefacts, resolution-dependent misrepresentation of narrow valleys, and shallow endorheic basins on surface flow routing, hydrographic model results based on both limited filling (z fill limit = 10 m) and unlimited filling (no z fill limit) were combined and reconciled, generating the final catchment extent.

Based on the geodata available for this study, several morpho-parametric datasets could be obtained (Table 2). The list includes morphometric measures commonly applied in geomorphological studies (see e.g. Bowman, 2019b, for an overview) for both alluvial fans (index f) and catchments (index c), including planar area (af and ac), radius (rf), perimeter (pc), and length (lc). Variable rf (fan radius) is defined as the longest distance from the apex, and lc denotes the longest distance within a given catchment measured from the catchment outlet.

Based on these fundamental variables, further data was derived, including mean center location (lat_f, long_f, lat_c, lon_c), landform relief (Rf and Rc), elevation (hf and hc), and gradient (gf and gc). All elevation and gradient data were obtained from swath profiles, with maximum elevation defined by the 90th percentiles to reduce topographic noise. Using the 90th percentile we obtained the most plausible and comparable results across our study area, e.g., by alleviating the impact of individual inselbergs on catchment metrics. Gradients were calculated as mean from individual section gradients, as defined by each elevation point along the swath profiles. The swath profiles were obtained by using the focal statistics tool in ArcGIS Pro on E-W rotated landforms, the rotation angle being defined by the angle between apex/pour point and landform mean geographical center. Large landforms that exceeded the input cell limit of the tool were processed in Matlab (ver. 2022b). Further indices were calculated for the watersheds: Basin-relief-ratio (rr_c), i.e., relief per drainage length (Patton and Baker, 1976; Schumm, 1956), Melton's basin ruggedness (Mc), the hypsometric integral (HI_c) to assess the geomorphic development of the catchments (Pike and Wilson, 1971; hypsometric curves were obtained using SAGA GIS ver. 9.7.1), and the circularity index (CI_c; Miller, 1953). Similarly to CI_c, previous studies used the fan length versus width to infer depositional environment characteristics (e.g. Bahrami, 2013a; Ghahraman and Nagy, 2024). In this study, we apply a similar approach, calculating the relationship between af and the theoretical area of a perfect half-circle defined by rf to approximate fan confinement (COI_f). To complement the alluvial landforms parametric dataset, the Sentinel-1 mean backscatter data was obtained for the mapped fan areas (S1_f). In a similar fashion, the CHELSA-BIOCLIM+ climate data (modern mean annual precipitation, Pc,mean, Pf,mean and maximum mean annual precipitation, Pc,max, Pf,max) was extracted for both the catchment and alluvial landform areas. For the catchments, the geological data from GSN (G1_c to G4_c) were extracted, and fault densities fd_c were calculated from total fault length fc,tot. Fault densities usually relate to tectonic activity, which over longer timescales can cause drainage reorganization (e.g. Bahrami, 2013b). On shorter timescales, significant fault movement and associated tremor can trigger mass movements (e.g. Crosta et al., 2014); both pathways may affect alluvial landform morphodynamics.

From the CHELSA-BIOCLIM+ precipitation data, precipitation peakedness (Ppk_f, Ppk_c) was calculated as the ratio between maximum precipitation and MAP, the former defined as the averaged maximum monthly precipitation (February or March in our study area), as outlined by Leier et al. (2005). Wind speeds were only obtained for the alluvial landforms (Wf,mean, Wf,max) to include potential effects of wind erosion on alluvial landform alteration. The dataset containing averaged relative frequencies of low cloud cover occurrence was clipped to both fan (FLC_f) and catchments (FLC_c). For the latter, a spatial limitation exists, as the accuracy of the data strongly declines at a distance exceeding about 100 km from the coastline (Hendrik Andersen, personal communication, 2023). We thus clipped the data to the 100 km range, implying that the largest catchments are not fully covered by FLC_c data. However, the generally strongly declining (advective) fog occurrence towards the hinterland (Olivier, 1995) indicate that low cloud cover frequencies beyond that boundary can be considered insignificant when compared to FLC_c to the west.

In hydromorphometric studies, common hydrographic parameters applied are related to the stream networks within the fluvial systems, with drainage density often used to assess the degree of landscape dissection (e.g. Howard, 1997; Collins and Bras, 2010; Mohren et al., 2020). The classic GIS-based approach of stream path determination relies on a noise-removed DTM used to generate flow directions and flow accumulations based on a minimum inflow value per pixel. However, especially in heterogenous hyperarid landscapes, characterised by ephemeral streams, different types of relief (mountainous to level), lithology (hard bedrock to unconsolidated sediments), surface cover (bare bedrock to encrusted), and patterns of fluvial erosion (v-shaped valleys to gullies), this standard approach often fails to capture the (present-day) stream networks as observed on true-color remote sensing data or in the field. For the Skeleton Coast of Namibia, difficulties in sediment routing mostly focused on the coastal and southern low-relief areas, which required the abovementioned merging of filled and non-filled drainage areas. As for the stream networks, streams in the low-relief areas appeared over-represented compared to the higher-relief areas, as commonly observed in similar studies (e.g. Mohren et al., 2020; Howard, 1997). To mitigate these issues, we applied a terrain morphology-based method to extract channel networks directly relying on valley detection by identifying and connecting concave-upward topography (Gao et al., 2022; Molloy and Stepinski, 2007). We calculated the tangential curvature for the GLO-30 DEM using a 5 × 5 moving window and kept all pixel values ≤ -0.0002 m⁻¹ to obtain a first representation of the drainage network. After vectorization, we filtered the individual patches of the drainage network by polygon circularity (CI, as defined in Table 2) and area a, using the threshold provided by Molloy and Stepinski (2007) to eliminate non-valley landforms (CI > 0.3, a > 20 pixels). The reconverted raster was then thinned and used to flag the stream network; all other areas were weighted by a value of -0.005 to allow flow accumulation fading when calculating the final topography-weighted stream network using the toolbox provided by Dilts (2015). As such, we obtained a stream network (representing the weighted flow accumulation < 200 pixels, i.e., ≈ 0.2 km²) that resembles the classic approach but puts less weight on the flat areas. The final stream lengths sc,tot were calculated including elevation data to account for 2D shortenings in steep terrain (see Howard, 1997). Since the stream networks include disconnected parts due to flow accumulation fading, no further hydromorphic metrics were obtained for this study. However, another parameter describing the sediment connectivity (IC_c) within the catchments (Walling, 1983) was obtained using the SedInConnect toolbox (ver. 2.3; Crema and Cavalli, 2018), with the non-filled DEM used for surface roughness and weighting factor estimation. Although the toolbox was designed to obtain sediment connectivity measures for high-resolution DEMs, it is also applicable to medium-resolution digital elevation data in comparative studies (e.g. Zanandrea et al., 2019; Gay et al., 2015; Walk et al., 2020).

The choice of parameters used in this study followed the rationale of compiling a pool of intuitive variables to describe the source-sink systems along the Skeleton Coast. To provide basic descriptive information, the data was first characterised by value ranges and distributional properties. A standard power-law relationship analysis was conducted (Eq. 1). However, given the pronounced heterogeneity of landforms and environmental conditions at both drainage and sink locations, a simple statistical description of individual variables from the bulk dataset would risk being misleading – or, in some cases, statistically unsound. To address this, we focused on reducing dataset heterogeneity, which can be achieved by cluster analysis.

Cluster analysis is an exploratory multivariate method that groups objects – in our case, alluvial landforms and catchments – in such a way that internal similarity within groups is maximised while dissimilarity between groups is increased (detailed descriptions of the method are provided by Backhaus et al., 2025a, and Cleff, 2019). Applied here, clustering provides a means to distinguish alluvial landform and drainage systems along the Skeleton Coast, with the potential to improve the robustness of subsequent statistical analysis and group-wise characterization.

To optimise clustering results, input variables should be independent and standardised to avoid the influence of (metric) scaling when distances between different groups are calculated. To achieve a suitable dataset containing variables relevant for clustering, we conducted a pairwise correlation analysis and excluded variables showing a strong interdependence (cutoff value defined by Pearson's correlation coefficient r > 0.7; cf. Backhaus et al., 2025b). In addition, the lithological data were transformed using the isometric log-ratio (ILR) method to achieve variable independency (Egozcue et al., 2003). Compared to other transformations (e.g., the centred log-ratio), ILR has been shown to yield more reliable results in exploratory multivariate analyses (Chen et al., 2019). Prior to transformation, zero values were replaced by a constant of 0.0001, and the relative contributions of the four lithology variables were adjusted accordingly. For clarity, we denote each IRL-transformed variable according to its numerator (G1_c,ILR, G2_c,ILR, G3_c,ILR; see Table 2).

Finally, the reduced variable set was tested for multivariate normality by calculating squared Mahalanobis distances and assessing variance with a chi-squared test (threshold value p = 0.001; calculated using SPSS ver. 29.0.2.0). While cluster analysis does not strictly require normally distributed input data (Cleff, 2019), the test can be used to flag potential multivariate outliers from the dataset.

Clustering was performed in Matlab (ver. R2024a) using the linkage function on z-transformed data. Given the comparably small size of the datasets we investigate, hierarchical clustering with subsequent k-means optimization was applied (e.g. Backhaus et al., 2025a). Both datasets – catchments and alluvial landforms – were clustered separately to identify possible correlation patterns between groups.

To determine robust cluster solutions, different combinations of proximity measures (similarity and distance) and agglomerative fusion algorithms were tested. Following the recommendations of Backhaus et al. (2025a), outliers were first removed using the Single Linkage algorithm with Squared Euclidean Distance. This step aims to improve the stability of subsequent clustering. The cleaned datasets were then re-clustered with alternative proximity measures and fusion algorithms, and the resulting dendrograms were evaluated visually and using the cophenetic correlation coefficient, which quantifies how well the dendrogram preserves the pairwise distances of the original distance matrix (Sokal and Rohlf, 1962; Gere, 2023).

The optimal number of clusters was determined with the Caliński and Harabasz criterion (Caliński and Harabasz, 1974). Among the candidate solutions, dendrograms containing more than three objects per cluster and the highest cophenetic coefficients were visually compared to assess the separation performance. The final clustering choice was based on a balance between (i) agreement with the number of clusters determined by the Caliński and Harabasz criterion and (ii) a reasonable cophenetic distance.

To objectively evaluate robustness, split-half test were performed: the datasets were randomly divided, clustered independently using the selected fusion algorithm and proximity measure, and then compared against the full-population cluster solution (Backhaus et al., 2025a). Only solutions that largely reproduced the population clusters were retained. Afterwards, k-means optimization was conducted using the kmeans function in Matlab.

The interpretation of the resulting clusters relied on t- and F-statistics to evaluate how well variables were represented within each cluster relative to the total population and to assess within-cluster homogeneity (Backhaus et al., 2025a). In addition, boxplots were used for visualization, and the spatial distribution of clusters was examined for contextual interpretation. To further investigate linkages of clusters and variables (hereafter termed “supportive”), partial correlation analyses were performed on log-transformed data at the 95 % significance confidence level. Special attention was given to commonly (hereafter termed “classical”) investigated morphometric relationships defined by Eq. (1), namely. af(ac), gf(ac), and gf(Mc), to identify variables influencing theses correlations.

From our mapping efforts a total number of n = 67 alluvial landforms could be identified along the Skeleton Coast of Namibia. Of these, n = 52 landforms could be delineated with sufficient confidence (mapping quality grades 1–3). For clustering, we considered both catchments and alluvial deposits separately to maximise comprehensiveness. Accordingly, we provide statistical analyses for both the full dataset (hereafter referred to as “catchment dataset”) and the quality-filtered dataset (hereafter referred to as “fan dataset”). An overview of the number of landforms retained after the different workflow steps we applied, and the counts used for display in our figures, is provided in Table B2 in addition to the information given in the main text and figure captions.

Statistically, both Kolmogorov–Smirnoff and Shapiro–Wilk tests indicate that the majority of variables deviates from a normal distribution. At the p = 0.05 significance level, the null hypothesis of normality could only be accepted for gf, Wf,mean, Wf,max, HI_c, dd_c, G1_c,ILR, and G2_c,ILR (Table B3). Consultation of histograms, boxplots, and QQ-Plots generally confirm these test results, with the exception of hc,mean, Mc, and IC_c, which appear to be reasonably normally distributed despite contrary test outcomes. However, caution is required when interpreting mean values and standard deviations for individual variables (Table B3).

The catchments analysed in this study are located between 17.6–21.6° S and 12.1–15.6° E, with areas ranging from ≈ 4 to ≈ 29 000 km², with other metrical variables (pc, lc) showing similar ranges on a relative scale (Figs. 1, 3a, Table B4). Likewise, catchment relief varies from 85 to 2380 m. These large ranges decrease for the derivates and indices obtained from the morphometrical data: Melton's ruggedness index Mc averages at 0.04 ± 0.01. The maturity index HI_c (0.44 ± 0.09) and the corresponding hypsometric curves (Fig. 3b) generally indicate mature to monadnock stages of drainage evolution (sensu Strahler, 1952a). The Messum catchment (alluvial landform IDs #62.1 and #62.2) is a notable outlier (HI_c = 0.21), as its upstream drainage portion incises the Brandberg massif (hc,max ≈ 2500 m a.s.l.). The Brandberg is also drained by the Ugab river (#57) and catchment #66, but their larger lateral extents balance hc,min over surrounding level areas, preventing similar low HI_c values.

Regarding the alluvial landforms, elevation-based grouping is evident from hf,max (Fig. 3c). Deposits located in the northern parts of the Skeleton Coast tend to terminate distant from the coastline, whereas southern fans tend to reach the Atlantic. Central alluvial deposits group as they are blocked by the Skeleton Coast erg. Approximately half of the landforms terminate proximally, i.e. at a distance ≈ 4–37 km from the coastline (suffix type S in Tables 1, B5). The other half reaches the beach area (suffix type A). Only a fraction occurs as single alluvial fan (n = 9, prefix type A), with more than 80 % of the landforms being confined. A minority are classified as polygenetic (n = 11, prefix type P) or constituting exclusively a (sub-) recent channel of an alluvial fan (n = 4, prefix type T0). The strong confinement of alluvial landforms is also reflected by COI_f, ranging between values of 0.08 and 0.64 (median 0.24).

The largest fan in our dataset is the Koigab fan (#44, 20.5° S; 133 km²), which is comparatively weakly confined (COI_f = 0.43). The smallest mapped alluvial landform covers an area of 0.3 km² (#33, rf = 0.8 km). Several landforms exhibit dataset extremes: the upper Sechomib fan (#11.1; 18.3° S) has the largest fan radius (18.5 km) and receives the highest amount of annual precipitation (90 mm, excluding fog). A minimum amount of annual precipitation of about 20 mm at fan #67 (21.9° S) illustrates the hyperarid conditions at the Skeleton Coast. This finding is underscored by the lowest Pf,max value of the dataset (49.1 mm) and lowest precipitation peakedness (2.5) found at the location of fan #67. The largest values for fan-wide averaged maximum precipitation (471 mm) and Ppk_f (5.2) are found in the opposite (i.e., northern) direction, at fan #2 (17.8° S). Nearby, the lower Sechomib fan (#11.2, 18.5° S) has the highest relief (333 m). The highest backscatter value (-11.8) from the Sentinel-1 data is recorded for the Gui-uin basin (#17.2, 19.4° S; lowest: -19.92, #11). Likewise, the lowest relief (4 m) is recorded there (#17.1, 19.4° S).

Overall, alluvial landforms along the Skeleton Coast show a mean gradient of 0.014 ± 0.06 m⁻¹ (1.4 % or 0.8°). Wind speeds average at 4.2 ± 0.6 m s⁻¹ annually, with maximum annual wind speeds being statistically similar (4.6 ± 0.7 m s⁻¹).

Fan dataset relation of af, ac, and gf, by means of Eq. (1) reveal af(ac) and gf(ac) power-law relationships significant at the 95 % confidence level (r2 = 0.14 and 0.49), with x1 = 3.79 and y1 = 0.24 for af(ac), and x1 = 0.03 and y1 = -0.17 for gf(ac), respectively (Fig. 3d). The gf(Mc) relationship is also significant (r2 = 0.36), with x1 = 0.11 and y1 = 0.66.

Following the scheme of Backhaus et al. (2025a) for cluster analysis, highly pairwise-correlated variables (r > 0.70) of the fan and catchment datasets were eliminated. This approach left n = 22 variables, with n = 8 variables describing the mapped alluvial deposits, and n = 14 variables describing the catchments (Table B6). Most reduction is caused by strong correlations between climate variables, geographical location, and elevation. Apart from precipitation peakedness (Ppk) and the excluded geographic/elevation variables, no linear bivariate relationships between alluvial landform and catchment variables were identified. Both fan and catchment datasets approximate multivariate normality, although systems #3, #27, #44 (Koigab), and #57 (Ugab) could be flagged as potential outliers (Tables B7 and B8).

Before discussing patterns of alluvial deposition along the Skeleton Coast of Namibia, we briefly evaluate the performance and reasonability of our methodological approach. This evaluation rests on (1) the choice of input data and (2) the cluster reasonability and robustness (e.g. Backhaus et al., 2025a).

A central source of uncertainty lies in the different spatial and temporal integration scales of the datasets. More specifically, catchment morphometrics and geological parameters integrate over topography-building timescales, whereas climate variables and, to some extent, alluvial landform morphometrics may reflect shorter-term conditions. The latter is amplified by post-depositional alterations, as many deposits along the Skeleton Coast likely predate 100 ka (Scheepers and Rust, 1999; Stollhofen et al., 2014) but have since been affected by other processes such as coastal erosion (e.g. Miller et al., 2021) and erg confinement (e.g. Krapf, 2003). However, such mismatches are not unique to our study but common in alluvial fan research, and despite them, fundamental scaling relationships – such as fan area and gradient versus catchment area or Melton's ruggedness index (Eq. 1) – generally appear to remain robust (see the global review on dryland fans provided by Woor et al., 2023a). Nevertheless, we acknowledge that the varying degrees of alluvial landform confinement in our study area impose a limitation when using planar fan area af as a key morphometric variable to interpret source-to-sink coupling. A potentially more meaningful metric could, in principle, be derived from fan thickness and/or volume. Unlike af, such measures may capture the influence of confinement on fan progradation and aggradation more sufficiently, and thus relate fan sediment storage more adequately to their drainage systems. However, owing to the diversity of depositional settings, irregular fan geometries, and uncertainties in the morphology of the underlying bedrock surface, we are unable to provide such a proxy with a level of accuracy comparable to that of af. We note, however, that the two-dimensional area of the individual swath profiles – bounded by their minimum and maximum elevation curves – shows a strong linear relationship with af (r = 0.92 for n = 67 landforms; Fig. C10). It therefore seems likely that metrics incorporating fan thickness would also be strongly correlated with af, and thus fail the initial variable filter step described in Sect. 3.4. An implication would be that these metrics would not provide a significant gain in morphometric information for the approach we follow.

Regarding climate, a certain variability in synoptic patterns during the Quaternary is evident for southern Africa (e.g., Stuut and Lamy, 2004; Stuut et al., 2002; Heine, 2004, 1998). Although past less arid phases promoted more active fan formation, relative gradients in moisture between coast and hinterland probably persisted throughout the Quaternary (see paleoclimate models for southern Africa of Heine, 1998, and Blümel, 2013). Despite model and downscaling-depended uncertainties, a glimpse in glacial climate conditions across our study area is provided by the CHELSA-TraCE21k dataset, which is based on the Community Climate System Model Version 3 and a reconstructed paleo-orography for that time, downscaled to a spatial resolution of 1 km (Karger et al., 2020, 2023). From here, dividing modern (Brun et al., 2022a) by LGM (Karger et al., 2023) precipitation model data (Pc,mean; LGM data prepared as described in Sect. 3.3) yields relative catchment-wide change factors ranging from ≈ 0.6 (#55) to ≈ 1.2 (#2), with a mean value of 0.9 across the investigated drainage areas (Fig. C11). Values < 1 therefore indicate higher (modelled) precipitation during the LGM, suggesting slightly less arid conditions in our study area, with a spatial focus to the near-coast catchment areas. More importantly, the LGM precipitation gradient towards the hinterland generally mimics the gradient presented by modern precipitation data.

Analogously, fog advection patterns may have followed broadly comparable gradients in the past. However, the modern climate dataset used in this study relies on gauge-corrected European Centre for Atmospheric Research (ECMWF) climatic reanalysis interim (ERA-Interim) data (Brun et al., 2022a, b; Karger et al., 2017), which does not account for precipitation from fog (Träger-Chatterjee et al., 2010). Large-scaled climate models tend to provide contradictive data at Namibia's coastline (see Karger et al., 2017) and generally fail to capture low-intensity precipitation from fog in a sufficient manner (Hemp and Hemp, 2024). This is problematic in the Skeleton Coast setting, given that fog constitutes a major water input (e.g., Li et al., 2018; Lancaster, 1984), contributing to the preservation of alluvial surfaces by cementation (Sect. 2). As an attempt to overcome the missing information on fog input, we used the independent dataset provided by Andersen and Cermak (2018). Yet, its short observational record of approximately three years introduces substantial uncertainty when drawing conclusions from modern spatial patterns with respect to long-term topographic evolution, and it did not provide information of significant value for the catchment areas (Sect. 4.1, Table B6).

As valid for the other modern climate parameters applied in this study, timescale-related uncertainties are inevitably attached to the wind data we used. There are indications that wind regimes may have varied during the Quaternary (e.g., Stuut and Lamy, 2004; Gingele, 1996), providing arguments for a late Quaternary formation of the Skeleton Coast Erg (Miller et al., 2021; Krapf et al., 2005; Sect. 2). However, given the strong role of the erg in shaping fan morphology, wind must be considered a relevant driver for morphometric analysis, even on modern timescales.

Evaluating the cluster analyses as conducted in this study, cluster performance depended strongly on outlier handling. Partial removal of outliers identified by single linkage fusion yielded cophenetic correlation coefficients of 0.64–0.65. While these coefficient values are moderate compared to other applications (e.g., > 0.8 in Santi Malnis and Rothis, 2024), they are within the acceptable range for exploratory clustering (cf. Gere, 2023). Especially in the catchment dataset, complete removal of the Cc₄ outlier cluster did not improve cluster recovery, as confirmed by split-half tests.

The fan dataset showed similar behaviour: Ward's linkage produced lower cophenetic correlation (0.64) than complete linkage (0.72) but yielded more reproducible cluster in split-half tests. This indicates that split-half evaluation is the more meaningful measure of clustering robustness in our context. Limitations are nevertheless evident in imperfect cluster recovery, elevated cluster F-values (Tables 3 and 4), and wide within-cluster variable value ranges (Figs. 7 and 8). In this regard, especially Cf₂ and Cc₂ can be considered as transitional clusters, while a clearer separation is achieved between Cf₁ and Cf₃ as well as Cc₁ and Cc₃. This finding is supported by the strong heterogeneity in Cf₂ alluvial landform types (Table 1). Given the substantial population share of cluster Cf₂ and Cc₂ (21 % and 37 %, respectively), more rigorous outlier removal could have been justified. At least for the catchment dataset, however, a thorough outlier removal would have resulted in two strongly heterogeneous clusters (as suggested by the Caliński and Harabasz criterion). Furthermore, the important metric capturing the fan gradient (gf) is distinctly separated between the catchment clusters (Fig. 7a).

An interesting insight into the clustering procedure is illustrated by the separation of fans #62.1 and #62.2, and #11.1 and #11.2. Both #62 landforms belong to the Messum drainage (21.4° S) and are characterised by very similar precipitation and wind conditions (< 16 % difference in Wf,mean and Ppk_f), gradient, and surface roughness (10 % difference in S1_f and gf). On the (sub-)catchment scale, both systems were identified as outliers and removed from analysis, as only (sub-)catchment area and mean elevation differ by ≈ 16 %. Regarding the alluvial landforms, greater differences are evident for fan size af (17 %), fan confinement COI_f (37 %; #62.2 < #62.1), and fan relief Rf (56 %). The largest differences, however, are encountered for low cloud cover frequencies FLC_f (90 %) and minimum elevation hf,min (100 %), both variables being dictated by the proximity to the Atlantic Ocean. Both variables represent strong cluster variables in Cf₂, with hf,min indicating an extremely low scatter. While these differences explain why #62.1 was assigned to cluster Cf₂ and highlight the discriminating power of individual variables, they provide to some extent justification for a separate treatment of these systems.

A contrasting scenario is evident for the Hoanib/Gui-uin subsytems (#17.1, 17.2). Here, differences of more than 30 % are evident for most variables (af, COI_f, Rf, gf, FLC_f), but both alluvial landforms were classified as outliers. This finding can be argued to reflect the unusual, wetland-like and strongly vegetated depositional setting in the basin (Stanistreet and Stollhofen, 2002), highlighted by exceptionally high Sentinel-1 backscatter values from vegetation and elevated electric conductivity (see e.g. Gupta, 2018 for details on the method). At the catchment scale, the close similarity of the nested subcatchments (< 4 % differences across all variables) explains their joint assignment to cluster Cc₄. These examples demonstrate that despite the existence of transitional clusters, the applied clustering approach is robust and meaningful. In particular, the clear differentiation according to fan type supports the validity of the procedure.

It should be noted that fan cluster Cf₂ includes many of the fans that have been in focus of research at the Skeleton Coast (Koigab #44, Ugab #57, and lower Messum #62.1), but does not include the Salt (#49) and Horingbaai (#63) fans, which have been described as fans very similar to Koigab and Messum by means of size, gradients, deposits (gravels) and primary morphodynamic process type (braided-river dominated; Krapf et al., 2005). Our cluster approach, however, groups the Salt and Horingbaai fans in Cf₁, which does not show any further notable correlations except for the gf(Mc) power-law correlation. The regression, however, is remarkably similar to the gf(Mc) relationship obtained for cluster Cf₂ and the bulk fan dataset (Table 6), bridging the two clusters in this regard.