<figure><img src="image_1.png" /></figure>

# A new workflow for mapping dune features (outline, crestline and defects) combining deep learning and skeletonization from DEM-derived data

Jimmy Daynac<sup>a, *</sup>, Paul Bessin<sup>a</sup>, Stéphane Pochat<sup>b</sup>, Régis Mourgues<sup>a</sup>, Samuel Shumack<sup>c</sup>

## ARTICLE INFO

### Keywords:

- Automated dune mapping

- DEM

- Deep learning

- Morphometric database

- Crestlines

- Defects

## ABSTRACT

Dune morphology, dynamics, and spatial arrangement mainly depend on the characteristics of the moving fluid (e.g. wind regime) and of the sediment supply (e.g. grain size) modulated by surface conditions (e.g. vegetation). A comprehensive mapping of dunes could provide essential and quantitative information for characterizing, analyzing, and monitoring dunes, dune patterns, and dynamics. This would help in understanding the underlying processes, from individual dunes to extensive dune fields. Here, we present a new workflow for the automated mapping of three dune features (outlines, crestlines, and defects) in GIS, based on DEM derived data (Residual Relief and Volumetric Obscurance; Copernicus 30 m DEM) and suitable for morphometric analysis. We first adapted a U-Net convolutional neural network (CNN) to map dune outlines. We then used a skeletonization tool to map dune crestlines. Crestline networks were then used to refine the individualization of coalescent dune outlines from a region-growing algorithm, while dune defects were mapped using a network topological analysis tool. Accuracy assessments demonstrate the efficiency of outline mapping from CNN (recall = 87 %, precision = 90 %, quality = 69 %) and we identified the limitations related to i) input DEM resolution, ii) training samples definition, and iii) skeletonization threshold settings. Finally, the application of the workflow to the Rub'Al Khali sand sea produced a map of 122,522 dune outlines/crestline networks and 514,083 defects, which were used for morphometric mapping and analysis (mean dune height, mean dune volume, defect density, and crestline density). Preliminary results demonstrate the robustness of the workflow to produce a large cartographic database suitable for morphometric analysis through its consistency with previous investigations while providing further uniformly detailed information. This workflow offers promising prospects for quantifying and understanding driving factors and boundary conditions, monitoring dune dynamics, from single dune to dune fields, including superimposed dune patterns of different scales where very high-resolution DEM are available.

## 1. Introduction

Dunes are formed through the accumulation of sediment grains transported by a fluid and can be defined as mobile mounds or ridges whether or not their slip faces are visible (Bagnold, 1974). Their shape, size, spatial arrangement, and displacement are related to the characteristics and interactions between the moving fluid and sediment supply modulated by surface conditions (Bagnold, 1974; Fryberger and Dean, 1979; Allen, 1982; Ashley, 1990; Wiggs et al., 1996; Andreotti et al., 2002; Ewing et al., 2006; Kocurek et al., 2010). In aerial or subaqueous environments on Earth, dune fields display dunes of different scales and often varying orientations, from ballistic ripples (cm scale) to individual

simple dunes (10–1000s m scale), and to compound and complex dune superpositions over dune fields (km to 100 s km scale). These latter are related to the coexistence of different flow regimes (Ashley, 1990; Ewing et al., 2006; Derickson et al., 2008; Wang et al., 2020) and/or to interactions and feedbacks between growing dunes and fluid flow (ratio between the thickness of the boundary layer and the bedform height) (Andreotti et al., 2009).

The production of detailed maps of individual dune features, together with morphometric analysis, could provide useful information for better understanding and characterizing dunes and dune fields (Zheng et al., 2022; Hugenholtz et al., 2012). This includes analyzing dune interactions and patterns (e.g. Ewing and Kocurek, 2010; Ewing

<footnote><sup>a</sup> Laboratoire de Planétologie et Géosciences, LPG UMR 6112, CNRS, Le Mans Université, Univ Angers, Nantes Université, Avenue Olivier Messiaen, 72085 Le Mans, France</footnote>

<footnote><sup>b</sup> Nantes Université, Univ Angers, Le Mans Université, CNRS, Laboratoire de Planétologie et Géosciences, LPG UMR 6112, 44000 Nantes, France</footnote>

<footnote><sup>c</sup> Climate Friendly Pty Ltd, Sydney, NSW 2000, Australia</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: jimmy.daynac@univ-lemans.fr (J. Daynac).</footnote>
et al., 2015; Day and Kocurek, 2018) or monitoring dune dynamics when sequential data are available (e.g. Lorenz et al., 2013; Yang et al., 2019). However, mapping dunes accurately and consistently across the entire field is a challenging task (Podwysocki et al., 1975; Siegal and Short, 1977; Hillier et al., 2015), as in aeolian environments, where no single universally accepted dune classification exists, despite recent research efforts (Scuderi, 2019; Zheng et al., 2022; Courrech du Pont et al., 2024). Considering the availability of DEM and satellite image datasets with an ever-increasing spatial (and temporal) resolution, such analyzes require automated mapping as manual digitizing i) is time-consuming and ii) could be of non-uniform subjectivity and quality because human operators cannot follow similar mapping criteria over large study areas especially when dealing with complex patterns.

During the past decade, several approaches have been proposed to automatically map dune map features (e.g. outlines, lee sides, defects), in either aeolian or subaqueous environments on Earth and Mars, from various datasets (e.g. ASTER 30 m DEM (Cazenave et al., 2013), CTX images (Vaz et al., 2015) or high resolution LIDAR DEM (Baughman et al., 2018)). Three distinct types of approaches can be identified (see SM1 for a compilation):

- Raster filtering and thresholding approaches where point, edge, or region detection filters are applied to Land Surface Parameters (LSP; e. g. slope, curvature, or residual relief), and terrestrial and martian images (e.g. Landsat Images; HiRISE respectively) to enhance dune features; and are then segmented into object features using thresholding values (Cataño-Lopera et al., 2009; Ghadiry et al., 2012; Telfer et al., 2015; Debese et al., 2016; Baughman et al., 2018; Scuderi, 2019; Wang et al., 2020). Some studies used spectral analysis (Cazenave et al., 2013; Wang et al., 2020), wavelet transforms (Cataño-Lopera et al., 2009), Radon spectrum (Gadhiraju et al., 2014), and spatial cross-correlation (Duffy and Hughes-Clarke, 2005) to extract specific dune parameters, such as dune asymmetry and crest direction.

- Image analysis approaches based on geomorphological phenotypes where image segmentation algorithms (e.g. multi-resolution segmentation) are applied to DEM data or LSP to segment object features and then calculate a set of parameters to the objects to classify them (Vaz et al., 2015; Emran et al., 2020; Stammler et al., 2022). Interestingly, several publications used rule-based models to classify neighboring pixels into basic relief features (e.g. slope, peak, flat, valley) and then group these features into crestlines, throughs, outlines, or sides (Di Stefano and Mayer, 2018; Cassol et al., 2021, 2022).

- Artificial intelligence and supervised (or semi-supervised) classification approaches where data-driven models are trained to detect or delineate dune features from terrestrial (e.g. Landsat) and Martian (e.g. CTX, HiRISE) images or DEMs. Commonly employed models include Deep Neural Networks (DNN) (e.g. Vaz and Silvestro, 2014; Foroutan and Zimbelman, 2017; Palafox et al., 2017; Nagle-McNaughton et al., 2020; Shumack et al., 2020; Rubanenko et al., 2021; Barrett et al., 2022) and Support Vector Machines (SVM) (e.g. Bandeira et al., 2011; Pradhan et al., 2018), and The latter regularly achieve highly accurate results (>90 %) and offer high transferability by simply replacing training data (Long et al., 2015; Marmanis et al., 2016; Yuan et al., 2020).

In this paper, we present a new workflow for automatically producing cartographic databases and maps of dune features (outlines, crestlines, and defects) from DEM-derived data, which are commonly used to perform morphometric analysis of dune fields. The workflow consists of two phases, focused on i) dune outlines mapping training a deep learning algorithm (U-Net CNN, Shumack et al., 2020), and ii) dune crestline, defects mapping and outline individualization using skeletonization, connectivity analysis, and region growing algorithm. The results present dune outline, crestline, and defects mapping performance and limitations from validation samples. Finally, we apply the

workflow to the Rub' Al Khali sand sea to test its robustness in producing a large cartographic database suitable for morphometric analysis.

## 2. Data and automatic mapping method

### 2.1. Conceptual and operational model for mapping dune features

To map dunes in numerical landscapes, their numerical definition, based on naturalistic descriptions can be conceptualized according to three morphological features commonly used to characterize dune mounds in the aeolian community: outlines, crestline, and defects (Wilson, 1972; Bagnold, 1974; Allen, 1982; Ashley, 1990; Edgell, 2006) (Fig. 1.A). To be relevant, the input digital dataset must: (i) have global coverage with sufficient resolution to ensure the reproducibility of the workflow and identify objects of interest, (ii) have minimal noise to improve workflow accuracy, and (iii) be generated from data acquired over as short a period as possible to reduce edge inconsistencies due to dune movement between adjacent raster tiles acquired at different times. Numerous land surface remote sensing data on Earth, such as DEM, are freely available and widely used due to their global spatial coverage and ever-increasing resolution (Hugenholtz and Barchyn, 2010). Currently, the highest terrestrial topographic data with global coverage is the ALOS DEM at 5 m resolution but only the 30 m resolution is free of charge. The Copernicus 30 m DEM dataset (Fahrland et al., 2022) was selected here because it outperforms other global DEMs at 1 arc-second (approximately 30 m resolution: ALOS (Tadono et al., 2016), ASTER GDEM version 3 (Abrams et al., 2020), NASA DEM (Crippen et al., 2016; NASA, 2020); SRTM (Farr et al., 2007; Guth and Geoffroy, 2021), and exhibits fewer edge inconsistencies upon visual inspection of the DEM or derived LSP, which are subsequently selected to extract dune features (outlines, crestlines, and defects).

The Residual Relief (RR) was selected to map outlines of dune mounds for its simplicity and its use in previous publications to manually map bedforms (Hiller and Smith, 2008; Hugenholtz and Barchyn, 2010; Majcher et al., 2020; Vérité et al., 2022). The RR identifies local mounds (dunes) and depressions from a DEM by assigning positive and negative values, respectively, while dune outlines are defined by inflection points in between (Fig. 1.B). RR is obtained by removing a regional relief signal (i.e. a smoothed surface) from a raw or pre-processed DEM using the following equation:

$$RR_i = z_i - \text{median}_{d_{ij} < \frac{x}{2}}(z_j) \quad (1)$$

where $z_i$ is the elevation of the focal cell $i$, $med_{d_{ij} < \frac{x}{2}}(z_j)$ is the median of elevation of all adjacent cells $z_j$ where the distance $d_{ij}$ between the focal and adjacent cell is less than half of $x$, the side dimension of the sliding window. The value of $x$ is set by each user with regards to the desired regional-scale relief signal to remove from the DEM to enhance dunes topographic signal (Fig. 2.A and 2.B).

A newly published LSP, the Volumetric Obscurance (VO) was selected to map dune crestlines and defects for its ability to clearly mark topographic slope breaks such as high-elevation inflection points within mound shapes that correspond to crestlines, while reducing the impact of noise (Loos and Sloan, 2010 adapted by Rolland et al. (2021, 2022)). The VO computes the ratio between the volume below and above the topography in a sphere of a given radius centered at a given point on the topographic surface (Fig. 1.D and 1.F), according to the following the equation:

$$VO_i = \frac{\sum_{j=1}^{n} Labove_j}{\sum_{j=1}^{n} Lbelow_j} \quad (2)$$

where $n$ sample points are placed randomly on a disc of radius $r$, centered on the focal cell $i$ and parallel to the best-fit regression plan.
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Natural and numerical dune representations. (A) Naturalist representation of a dune based on Bagnold (1974). (B) 3D representation of a dune on a DEM. (C) 3D representation of a dune outline using the Residual Relief (RR) (D) 3D representation of the dune crestline using the VO. (E) Residual Relief variations on a dune topographic (transverse) profile, dune outlines are defined by local low inflection points between positive elevation values. (F) Volumetric Obscurance variations on a dune topographic (transverse) profile, dune crestlines are defined by the junction of local high inflection points on a sphere of a chosen radius.</figcaption></figure>

The *Labove*<sub>j</sub> and *Lbelow*<sub>j</sub> length are measured between each sample point *j* and its projection to the surface of the above and below hemisphere, respectively, following the normal direction of the disc (Fig. 1. F). A vertical exaggeration factor can be used with the algorithm to enhance landforms. VO is expressed without units and ranges between 0 and 1, with values of 0.5 corresponding to flat areas, values tending towards 1 reflecting crestlines, and values tending towards 0 reflecting topographic throughs (Fig. 2.A and 2.C).

The workflow hereafter developed to map dune features (outlines, crestlines, and defects) is divided in two phases (Fig. 3). The phase 1 corresponds to dune outlines mapping using Deep Learning algorithm on RR input data. The phase 2 consists of crestlines mapping using a skel-etonization algorithm on VO input data, then defects mapping through network analysis of crestlines, and finally dune outlines individualiza-tion using region growing from crestline network seeds.

## 2.2. Phase 1 – Dune outlines mapping with a deep learning algorithm

### 2.2.1. U-Net convolutional neural network selection and adjustments

We selected a robust and simple deep Convolutional Neural Network (CNN) used for semantic segmentation and called U-Net (Fig. 4; Ron-neberger et al., 2015), since it has been modified by Shumack et al. (2020) to map and analyze stabilized linear dunes in Australia. After LSP preprocessing using an edge detection filter (Laplacian) and then a noise filter (Gaussian), data enters the U-Net CNN characterized by its U-shape consisting of two main convolution paths (Fig. 4). The first contracting path extracts essential information while compressing the input raster through downsampling, facilitating the identification of the numerical

solution (i.e the essential information). The expanding path de-compresses the raster through upsampling while learning to precisely locate outline the numerical solution through concatenation with the downsampling of the corresponding output. At the end of the learning process, an output segmentation map is generated (Fig. 4).

To perform dune outlines mapping, several adjustments are made from the Shumack et al. (2020) U-Net CNN. The initial DEM input data (AWD3D30) is replaced by RR to delete the regional relief signal and focus on dune-related relief while the dimension of the input data is increased from 96 × 96 pixels to 192 × 192 pixels to fully include large dune samples. Along the workflow, the CNN implicitly learns the RR value threshold used by the cartographer, as well as the RR value dis-tributions within outlines (e.g. slope, curvature), and the variability of the outlines (e.g. sinuosity, circularity).

### 2.2.2. Collection of training sample datasets

One hundred training areas covering different types of dune (e.g., star, barchanoid, dome, linear, and complex dunes) were clipped from RR raster of four arid regions (Algeria, Mauritania, China, Yemen; Fig. 5 and see SM2 for locations). Twenty of these samples include common non-dune landforms in desert environments (e.g., cliffs, bedrock, fluvial structures, Fig. 5) to train the CNN algorithm to distinguish between dunes and these landforms (Shumack et al., 2020). Each training sample is 192 × 192 pixels, set to cover the largest dunes on Earth using Copernicus 30 m DEM data at full resolution. To increase the morpho-logical variability of the dunes and enhance learning capacity, the res-olution of some samples is degraded. Specifically, 25 % of the samples have a resolution of ~30 m, 25 % of ~60 m, 25 % of ~70 m, and 25 % of

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Residual Relief and Volumetric Obscurance extraction concept. (A) Original DEM (left) and its topographic profile (right). The profile shows the steep regional relief on which a topographical signal corresponding to the dunes is present. (B) Residual Relief (20 pixels square matrix; left) and its profile (right); Red areas on the profile indicate positive local relief associated with the dunes. (C) Volumetric Obscurance (20 pixels radius; vertical exaggeration x 1000; left) and its profile (right); yellow gradient enhance of high inflection points associated with the crestlines.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Overview of the workflow for dune features mapping. Phase 1 performs dune outline mapping from RR using U-Net CNN. Phase 2 performs crestline networks and defects mapping from VO. Dune outline individualization is refined using crestline networks as seeds within a seed region growing algorithm.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 4. Schematic global U-Net architecture to map dune outlines. The preprocessing data undergoes a first convolution block within the contracting path, filtered by a Laplacian of Gaussian (LoG) filter. This includes executing two successive convolutions with ReLU activation functions, followed by max pooling to summarize pixel feature values. The expanding path concludes with the last transpose convolution block, which involves concatenating the matrix product from the previous transpose convolution with the matrix product from the second convolution of the first convolution block in the contracting path. The sigmoid activation function is the last activation function used to convert the numerical pixel values of our interest features into a binary raster. The binary raster describes a class probability: 0-pixel values as “no interest” (in black), and 1-pixel values as “dune outlines” (in white).</figcaption></figure>

~90 m. Moreover, these multi-resolution datasets allow us to optimize the adaptability of the predictive model, significantly improving the robustness of the neural network without any loss of accuracy (Zhou and Liang, 2023). This also enables the generalization of our method to datasets of different resolutions and the mapping of dunes of different sizes.

For each sample, the “ground truth” (e.g., dune outlines) was manually digitized and converted to a binary raster on a GIS (QGIS®) software. RR raster was calculated with a 20 × 20 pixels matrix square filter, which was visually set to preserve and enhance the widest dune on each sample (from 600 m to 1800 m wide, for 30 m to 90 m resolution, respectively). Then, the cartographer carefully delineated dune outlines (i.e. where RR = 0 m) along with a visual control of the occurrence of dunes on freely available satellite images (e.g. Google satellite XYZ tiles; Fig. 5).

### 2.2.3. Convolutional neural network training

The U-Net CNN was trained following Shumack et al. (2020) and Ronneberger et al. (2015). The training aims to reduce a binary cross-entropy loss function which evaluates the deviation between model predictions and “ground truth” in each training subset data, to optimize the model weights. The sample dataset was first split into training (n = 80) and validation (n = 20) subsets (see SM2 for the attribution datasets). Then, for each training sample, an epoch of 300 batch steps with five new samples per batch, generated from data augmentation by random deformation (shearing, shifting, flipping, rotation, and zooming), was created to increase the model robustness and limit the over-fitting probability. The model was trained for 100 epochs, and the optimal model weights were stored according to the loss function calculated on the training subsets.

### 2.2.4. Model evaluation

After training, the model is used to predict dune outlines from the validation subset to perform the model accuracy assessment. This accuracy assessment is derived from a confusion matrix (available in the SM) which provides information about model prediction and “ground truth” overlap using Recall (Eq. 3), Accuracy (Eq. 4), and Quality (Eq. 5) equation (Telfer et al., 2015; Lewington et al., 2019; Bianchi et al.,

2021):

$$ \text{Recall} = \frac{TP}{(TP + FN)} \times 100 \qquad (3) $$

$$ \text{Accuracy} = \frac{TP + TN}{(TP + TN + FP + FN)} \times 100 \qquad (4) $$

$$ \text{Quality} = \frac{TP}{(TP + FP + FN)} \times 100 \qquad (5) $$

where TP, TN, FP, and FN represent the number of true positive, true negative, false positive, and false negative predictions, respectively, between the “ground truth” map and automatic predictions.

## 2.3. Phase 2 – Dune crestlines, crestline networks and defects mapping

### 2.3.1. Dune crestlines skeletonization and crestline network identification

For dune crestlines segmentation, a VO raster was computed with a 20 pixels radius (consistent with the RR radius, cf. §2.2.2), and a × 1000 exaggeration factor to enhance high inflection points corresponding to crestlines (Rolland et al., 2022). The VO raster was then thinned to a branched skeleton corresponding to crestlines following the skeletonization approach published in Putniņš and Tveite (2021) and based on the QGIS® Thin Greyscale Image to Skeleton Plugin (TGS; Tveite, 2017) (Fig. 6.A). We selected this tool because of its top-down approach which first thins the higher-intensity VO intervals that then constrain the lower-intensity ones, i.e. it first extracts protruding crestlines and then extends them to their less protruding arms and branches. Here, nine sets of VO threshold intervals (0.1 intervals) ranging from 1.0 to 0.1 (Set 1) to 1.0–0.9 (Set 9) were empirically tested. The branched skeleton is transformed into polylines, then smoothed to reduce aliasing in the raster-to-vector conversion, optimizing the accuracy of geometric and topological analyzes (snake method (Burghardt, 2005)) (Fig. 6.B). Connected crestlines are then identified and grouped in crestline networks.

### 2.3.2. Dune outline individualization and defects mapping

We developed an automated protocol based on the NetworkGT QGIS® toolbox (Nyberg et al., 2018) using the QGIS® graphical modeler (i) to implement an automated analysis of crestline network connectivity and defects and (ii) to assign a branched crestline network to a
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Overview of the outline feature samples used for training the U-Net algorithm. Each sample consists of DEMs with a resolution of 192 pixels (~ 6 km) that display the dunes RR 20 pixels with different shapes selected from four deserts. Each dune's interest features are manually labeled with a green "ground truth" mask, which serves as the true reference for training the algorithm. Referencing is carried out with a visual control on satellite images of the presence of dunes (Google satellite XYZ tiles).</figcaption></figure>

given morphology to individualize outlines of coalescent dunes. Crestlines network topology consisting of branches bounded and connected by nodes (i.e. defects) was used for defects mapping. Each defect is classified using the NetworkGT QGIS® toolbox, depending on the number of branches it connects or not (Fig. 6.C) (Sanderson and Nixon, 2015; Nyberg et al., 2018; Manzocchi, 2002). Isolated defects (I) represent free terminations located at the ends of branches (Fig. 6.C) while defects connecting three (Y) or four branches (X) describe more complex connectivity with crestline bifurcations and interactions which can provide information about changes in boundary conditions such as wind regime shifts or sediment supply variations (Fig. 6.B & Fig. 6.C) (Day and Kocurek, 2018; Marvin et al., 2023).

Several dune fields show coalescent dunes (e.g., barchanoid dunes; Fig. 6.B) characterized by continuous positive RR values where outlines are not individualized from the Phase 1. However, distinct crestline networks extracted from VO raster (Fig. 6.E), provide an opportunity to refine dune outline segmentation. Considering that each crestline network belongs to a single dune outline, a seed region growing segmentation was performed on eCognition® to generate outline edges between coalescent dunes (Fig. 6.E), allowing the discrimination of individual dunes within complex patterns (Fig. 6.F). The output of individualized dunes is finally vectorized into polygons (outlines) then smoothed to reduce aliasing in the same way as crestlines.

### 2.3.3. Dune crestlines skeletonization evaluation

Both a quantitative (e.g. number of crestline networks and defects)

and qualitative (e.g. artifacts) evaluation of our dune crestlines skeletonization was carried out on the validation data used to validate the performance of the U-NET model. Crestlines and defects were extracted for the 9 sets of VO thresholds (1.0–0.1 to 1.0–0.9, 0.1 increments) for each validation sample.

## 2.4. Application on a desert scale: The Rub'Al khali sand sea

To test the performance and relevance of the workflow for geomorphological applications, we applied it to the Rub'Al Khali desert, the largest active desert in the world, covering about 660,000 km² and characterized by a diversity of dune forms (Breed et al., 1979; Edgell, 2006). We used the tools available in QGIS® to produce and analyze dune height, dune volume, defect density, and crestline density maps. These data were integrated into a 2.5 km hexagonal grid to facilitate visualization at the desert scale while preserving the accuracy of the cartographic details. Dune heights (m) and volumes (km³) were calculated using RR range and the surface area of each mapped dune while dune mean height (m) and mean volume were computed. Defect density (m⁻¹), defined by the ratio of the number of defects pairs of a dune to the cumulative length of its crestline (Werner and Kocurek, 1999), was here computed for each hexagon. Finally, crestline density (km.km⁻²), was calculated using the ratio between the cumulative length of the crestlines contained in a hexagon and the hexagon area.
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Concept of the crestline extraction and dune individualization. (A) Skeletonization of the dune using the "Thin Greyscale Skeleton" tool. The computation is performed on the Volumetric Obscurance (VO) output applied to the Residual Relief (RR). (B) The digital output produces a raster of raw branched crestlines. (C) The connectivity of the branched crest network is analyzed. The algorithm identifies and extracts nodes based on the number of occurrences of nodes at each endpoint and/or intersection of a polyline (in blue *I* = 1, in green *Y* = 3, and in red *X* = 4). (D). Merging of branched crests and nodes in contact with each other. The entity formed as a result of this fusion corresponds to a crestline network belonging to a given morphology. (E) The crestline network can be enlarged to create a physical boundary between neighboring crests. (F) The "Seed region growing" tool allows to separate the dunes within a complex shape (e.g., barchanoid ridges).</figcaption></figure>

# 3. Results: Workflow validation and limitations

## 3.1. Dune outlines mapping: U-Net performance

A mean recall of 87.1 % for a mean accuracy of 90.9 % and a mean quality of 69.1 % were achieved for dune outline predictions (see SM3 for all metrics per sample). These scores are comparable to those reported by Shumack et al. (2020) and Li et al. (2020), indicating a high percentage of correctly classified pixels.

After CNN training, predicted polygons closely match the shape of the underlying relief and the “ground truth” outlines with few unrecognized or disturbed features for both simple and complex dune shapes (Fig. 7). For samples that contain fluvial features (e.g. sample 23; Fig. 7) or substratum and rock cliffs (e.g. samples 29, 36, 39; Fig. 7), the model successfully dissociates the dune features from these ones. Where samples of the RR present lower relief features with a width close to the DEM resolution, the outline detection fails (e.g. samples 23, 30, 36, 39, and 93; Fig. 7). Indeed, such cases are globally found on samples with noisier topographic signals, reducing the probability of prediction and/or deforming the final shape of outline predictions (yellow arrows on Fig. 7). The distinction between “dune” and “no-dune” is based on the algorithm's analysis of pixel distribution: homogeneous for dunes, heterogeneous, rough, and noisy for no-dunes.

However, a qualitative assessment of the U-Net model predictions compared to residual topographic data reveals three main limitations (Fig. 8). The primary limitation arises from the chosen resolution settings with a DEM resolution of 30 m and a RR calculated on a 20 × 20 pixels sliding window, the smallest observable dunes must be at least 600 m in length and width to be significant for potential geomorphological analyzes (indicated by the blue arrow in Fig. 8.A and 8.B). Non-significant morphologies below this threshold are deleted and not represented here. However, the neural network may struggle to identify the smallest observable dunes on this RR input data, possibly due to inadequate highlighting by the Laplacian of Gaussian kernel during U-Net training (Shumack et al., 2020).

The second limitation involves the local underestimation of dune outlines for RR calculated on 20 × 20 pixels sliding window (indicated by the green arrow in Fig. 8). This false negative prediction results in an incomplete segmentation of dunes by the neural network. This discrepancy can be partly due to the challenging distinction between the positive relief of the dunes and the substrate, which may be less pronounced, particularly in sandy interdune areas (as illustrated in the shaded DEM of Fig. 8.C and 8.D), whereas in the case of dunes with limited sand input, their borders are clearly discernible (Fig. 8.E).

The last limitation is the local overestimation of dune outlines observed compared to the underlying topography (marked by the pink
<figure><img src="image_10.png" /><figcaption>Fig. 7. Visual test subset composed of 20 % of the outline feature samples, their manual references, and predictions. The "subset" column shows a RR red gradient of the dune samples illustrating their outlines. The "ground truth" masks are manually labeled (green masks) and serve as the true reference. The last column shows the binary prediction of the dune outlines after training and testing on the samples. The samples 20 to 39 contains no-interesting features such as rock cliffs, substratum, or fluvial features. Yellow arrows show noisy topographic signals leading to prediction errors and/or deforming the final shape of outline predictions.</figcaption></figure>

arrow in Fig. 8). Although the “ground truth” outlines manually defined on learning samples only contain positive RR values, the CNN implicitly learned the relationships between neighboring pixels (e.g. slope, shape) and assigns weight to them. Consequently, the weights of these relationships are often greater than the RR values when applied. This is more pronounced where dunes begin to merge into patterns or where there is background noise, which challenges the accuracy of manual reference mapping (Fig. 8.C and 8.D) (Shumack et al., 2020).

To increase the precision of U-Net, the “ground truth” outlining of dune could be first improved. In this study, reference data was developed by a single operator, introducing a unique interpretation of what constitutes a dune. This gap could be filled by creating multiple training sample sets based on various manual interpretations from different specialists working on the same training samples. This approach may bring a wide range of variations and edge cases, helping U-Net to generalize better and handle unexpected inputs more effectively. Multiple operators can design more diverse dune outlines to cover underrepresented scenarios, reducing potential biases and leading to a more balanced and fairer model. By focusing on specific areas, such as highly intricate aeolian dunes, particular weaknesses that U-Net might overlook can be addressed. This approach provides high-quality data that targets and improves performance in critical areas, resulting in a deeper understanding and better recognition capabilities. Paradoxically, the variability introduced by different human operators, which mimics the unpredictability of aeolian dunes, may make U-Net more robust and

adaptable to changing or unforeseen conditions during real desert applications. This would allow for a more precise definition of dune contours and reduce the error associated with a single individual's interpretation. Ultimately, collaborative work among several experts in aeolian processes on these training samples could lead to the production of increasingly accurate maps. However, it is important to note that multiplying interpretations of dune outlines also lead to increased uncertainties in dune delineation, which can vary from one operator to another. Indeed, according to Smith and Clark (2005), cartographic error by a single interpreter can be relatively low, while the variation between operators can be high.

## 3.2. Dune crestlines mapping performance and threshold value setting

Dune crestlines, networks, and defects extraction were performed using nine sets of skeletonization thresholds ranging from 1.0 to 0.1 (Set 1) to 1.0–0.9 (Set 9), reflecting different levels of dune complexity (e.g. superimposition). To analyze the influence of threshold settings on extraction, they were calculated on the same validation samples used to validate the U-Net model (see SM4 for a complete set of skeletonization metrics). The analysis shows that the number of defects decreases as the number of thresholds decreases, i.e. when confined towards high VO values while the number of individualized crestline networks and individualized dune outlines increases as the number of thresholds decreases, and vice versa (Fig. 9, SM4). For example, on the validation
<figure><img src="image_11.png" /><figcaption>Fig. 8. Qualitative evaluation of the U-Net model performances and prediction limits to the residual topographic data and resolution across different dune configurations. Notable gaps in the cartographic output include (i) insignificant dune omitted due to the resolution limit (blue arrow), (ii) underestimated outlines (green arrows), and (iii) overestimated outlines (pink arrows)(Satellite images from Google Satellite XYZ tiles).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Illustration of the impact of the choice of skeletonization threshold value on the complexity and number of (A) crestlines and nodes (in blue “I”, in green “Y”, and in red “X”), (B) crestline networks, (C) individualized dunes. The numbers under each illustration are representative of the number of objects generated at the sample level. The crestline networks’ colors and their “Id” represent the generated entities diversity.</figcaption></figure>

sample 75, a threshold set of 1.0–0.1, i.e. accounting for high to low VO values, generates many defects (Fig. 9.A; 168 defects generated) but few individualized crestline networks (Fig. 9.B; 10 different networks). Consequently, there are fewer individualized dunes when refining the segmentation of dune outlines using the Seed Region Growing algorithm (Fig. 9.C). However, a set of thresholds of 1.0–0.9 accounting for high VO values, captures the highest topographic points, generating fewer defects (Fig. 9.A; 52 defects generated) but more crestline networks and thus more individualized dunes (Fig. 9.A; 26 different networks).

The choice of an optimal set of threshold values remains delicate and depends on two criteria: the geomorphological nature of the studied object (dunes in this study) and the resolution of the input data (Putniņš and Tveite, 2021). Defining a single value suitable for all situations is probably not possible, nor even desirable about these criteria and the morphological diversity of dunes, as it is not necessarily true that the value defined in a given region is optimal for all dune fields (Telfer et al., 2015). Opting for a set of thresholds reaching low VO values can be judicious to capture the full complexity of morphological features, described by greater branching and an increased number of defects (Fig. 9). However, it introduces errors and artifacts, mainly localized in the smoother and flatter interdune surfaces to related to background noise (Fig. 9). In this context, Putniņš et Tveite (2021) recommend choosing a set of thresholds confined to high VO values, which is more suitable to minimize the impact of noise. However, it is essential to note

that this choice induces a reduction in the individualized surface, complexity, and connectivity of the objects (Fig. 9). Thus, the operator must choose a balance between two opposing trends choosing sets of thresholds: those including low VO values that bring out the full complexity of the dunes but tend to detect background noise, and those confined to high VO values that allow a simplified description of crestlines but, at the same time, prevents the identification of a large number of dunes. Given the limitations previously described and observations from the visual inspection of various thresholds, we find that quantitative justifications for determining the optimal threshold are not yet fully established. Nevertheless, in the context of our study using the Copernicus DEM (30 m), visual analysis suggests that thresholds ranging from 1.0 to 0.6 (Set 6) are best suited. This set allows us to capture the complexity of crestlines while avoiding interference associated with thresholds that are too low (increased background noise) or too high (loss of significant information) (Fig. 9). However, it is essential to be aware that the worldwide variability in dune shapes, size, and topographic characteristics necessitates a flexible approach to determine skeletonization thresholds based on the desired level of detail and the object of study.
# 4. Application and discussion: The Rub'Al khali sand sea

## 4.1. Morphological map production

The application of the workflow to the Rub'Al Khali sand sea, using the same configuration (RR, VO and thresholds) and exclusion of non-significant dunes (< 600 m of width and length), produced a map of 122,299 dune outlines covering 161,577 km², 122,299 crestline networks covering 247,697 km, and 514,083 defects, trained, produced and cleaned in less than a week (Fig. 10.A). Visual inspections of the results show that dune outlines, crestlines, and defects were accurately mapped (Fig. 10.B & 10.C), revealing the dune patterns and the morphological diversity and complexity observed in shaded relief. Consistent with workflow limitations previously identified (§3): i) some over- and underestimation of dune outlines are observed, and ii) some dunes are omitted because they are too small with regards to the data resolution or have low RR values compared to the model training data (SM). One area in particular illustrates this latter limitation. Located in the central north part of the sand sea (Fig. 10.A), dunes remain unmapped while sand sheets and streaks are identified by previous authors (Breed et al., 1979), because their reliefs are low in the DEM and RR input data.

## 4.2. Preliminary morphometric results

The morphological map output provides a substantial database of

dune outlines, crestlines, and defects (available in SM) for computing and analyzing dune morphometric variations and configurations at a sand sea scale (Fig. 11). A complete and thorough morphometric analysis and interpretation of the Rub'Al Khali desert is beyond the scope of this paper. However, we present preliminary results on dune mean height (Fig. 11.A), dune mean volume (Fig. 11.B), defect density (Fig. 11.C) and crestline density (Fig. 11.D). We compare these results to published works such as dune classification maps (Breed et al., 1979; Edgell, 2006); Fig. 11.E and F), and propose further investigations using such a database. To avoid reading bias, all the presented morphometric maps are built using sequential, continuous, non-distorting, and universally readable color maps (Crameri et al., 2020).

Dune mean height and dune mean volume maps provide information about sand supply distribution (Fig. 11.A and B). These maps show a main area of high sand accumulation, located east and southeast of the sand sea, with mean heights higher than 90 m and mean volumes ranging from 0.5 to 1.1 km³ grouped in a “Phrygian cap” shape (Fig. 11, location I). Conversely, the central north part shows low sand accumulation, with mean heights <30 m and mean volumes <0.15 km³ (Fig. 11, location II). The western part of the desert displays intermediate mean heights between 30 m and 90 m and mean volumes between 0.15 and 0.5 km³ (Fig. 11, location III). The mean height and volume distributions, and ranges of these dunes are consistent with the previous work of Almutlaq (2017) while the total dune volume here estimated is 8718 km³ and closely matches the estimations of Almutlaq et al. (2022). Some

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Dunes map of the Rub'Al Khali sand sea. A) Result of the digital output of the method which identified over 100,000 dunes, crestlines, and defects, representing a mapping of over 160,000 km² of positive relief and over 200,000 km of cumulative length crestlines. Focus areas illustrating in detail the automatic output is shown in focus B) for crescentic dunes, and C) for pyramidal dunes (Breed et al., 1979; Edgell, 2006).</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 11.** Example of preliminary morphometric investigations on Rub'Al Khali sand sea. The morphometric parameters computed on a hexagonal grid of 2.5 km at this scale with the protocol are: A) dune mean height, B) dune mean volume, C) defect density, and D) crestline density. Zone of interest are shown in the top left-hand corner. E) Breed et al. (1979) dunes classification. F) Edgell (2006) dunes classification.</figcaption></figure>
mean height and volume transitions are sharp and clearly identifiable in Fig. 11.A and B correspond to limits between dune classes mapped in previous work. The sharp transition between the central part of the sand sea (zone II) and the “Phrygian” cap (zone I) well illustrates the limits between crescentic (blue classes on Fig. 11.E and F) and linear dunes (yellow to brown classes on Fig. 11.E and F) of Breed et al., 1979 and Edgell (2006). However, variations in mean dune heights and volumes are smooth within the central part (zone II) and do not reflect the sharp limits delineated between sub-classes of linear dunes in these two previous works. Instead, they indicate a progressive morphometric transition, which could be interpreted as gradual morphological changes along with progressive changes in sand supply.

The defect density map (Fig. 11.C) provides information about dune interactions and patterns, because free termination defects migrate faster than the dune cores, inducing interaction defects (i.e Y junctions) when colliding with downwind dunes (Werner and Kocurek, 1999), and mainly reflect wind regime and sediment supply (Day and Kocurek, 2018). Here, the defect density ranges from $3 \times 10^{-5}$ to $1 \times 10^{-2} m^{-1}$, and is consistent with the order of magnitude of Shumack et al. (2020) (Simpson Desert, Australia: $5 \times 10^{-5}$ to $7.5 \times 10^{-3} m^{-1}$) and Ewing et al. (2015) (ranging from ca. $8 \times 10^{-6}$ to $1 \times 10^{-2} m^{-1}$) and show an inverted trend of values with regards to dune mean height and volume maps (Fig. 11). High defect densities, between $1.4 \times 10^{-2}$ and $1.6 \times 10^{-2} m^{-1}$, are located southeast of the sand sea (Zone I, south to the “Phrygian cap”) where Breed et al. (1979) mapped star dunes while Edgell (2006) recognized linear (“seif”) dunes (Fig. 11.E and F). Conversely, low defect densities, ranging from $3 \times 10^{-4}$ to $4 \times 10^{-3} m^{-1}$ occupy the southeast part of Rub’Al Khali (Zone III, Fig. 11.C) where linear dunes of mostly simple shapes are identified (Breed et al. (1979), Fig. 11.E). However, the defect density map shows i) more diffuse transitions between high and low-value areas (e.g. between Zones 1 and 2, around 20°N;53°E) together with i) a greater signal variability within each high or low-value area, clearly expressed by a “salt-and-pepper” effect (e.g. within Zone 2 and south of Zone 1, around 19°N;55°E).

The crestline density map provides a useful alternative to dune wavelength (Bullard et al., 1995) and spacing (Ewing et al., 2006). Crestline density values of up to $10 \text{ km.km}^{-2}$ and value shows a global similar distribution compared to defect density but with sharper transitions (e.g. between Zone 1 and 2; Fig. 11.C and D). However, closer observations reveal alternations of roughly WSW-ENE corridors of different crestline densities (ca. $4-5 \text{ km.km}^{-2}$ and ca. $2-3 \text{ km}^{-1}$ within the southeastern part of the sand sea (Zone III) traducing interactions of dunes of slightly different crestline orientation.

The combination of these morphometric parameters reveals that the high sand accumulation area (Zone I) shows low crestline density values, i.e. to widely-spaced dunes (Fig. 11), located where greater dune mobility driven by seasonal and multimodal winds, including Shamal and Kharif monsoon winds, is documented (Bishop, 2010). By contrast, the southwestern part of the desert (Zone III) shows lower sand accumulation and low defect and crestline densities (Zone III, Fig. 11) where long, pluri-kilometer linear dunes of ca. N60 orientation (Fig. 10.A, Breed et al., 1979; Edgell, 2006), but less mobile and less reoriented by the winds (Werner and Kocurek, 1997) are documented. The sand in this area is sourced from the Arabian Shield with similarities with the northeastern areas interpreted as a homogenization of deposits across the desert under the influence of Shamal winds (Garzanti et al., 2017). Dune crestlines are subparallel to these winds, maximizing the efficiency of sand transport (Cazenave et al., 2013) and dune stability while limiting dune mobility or reorientation (Werner and Kocurek, 1997). However, some dunes vary in orientation on the order of 10 to 20°, which could suggest local or seasonal adjustments in wind patterns (Cazenave et al., 2013).

## 5. Conclusions

An automated workflow to produce, maps and cartographic

databases of dune features (outlines, crestlines and defects) from DEM data and for entire deserts was presented. The workflow consists of 2 phases: i) dune outlines mapping from local relief data (Residual Relief) through the adaptation of deep learning approach (U-Net CNN) (Shumack et al., 2020) and ii) dune crestlines and defects mapping from skeletonization of high slope breaks using a new volumetric approach (Volumetric Obscurance, Rolland et al., 2021, 2022), followed by a network analysis.

Results on validation samples (recall = 87 %, precision = 90 %, quality = 69 %), confirm the reliability of the workflow while the main limitations encountered are due i) to the resolution of the initial data which controls the minimum scale of significant dunes that can be mapped, ii) to local over- and underestimation of dune outlines in U-Net predictions related to the outlines defined on training samples, and iii) to the setting of the skeletonization thresholds for crestline extraction, which depends on the scale of the objects of interest. Nevertheless, cartographic and morphometric results from the application of the workflow to the Rub’Al Khali sand sea demonstrate its reliability for analyzing complete active deserts, allowing the precise extraction of >100,000 dune outlines, crestlines and defects. Preliminary results illustrate the potential of the workflow to easily quantify morphometric parameters (height, volume, defect density, crestline density), offering promising prospects for quantifying and understanding dunes and dune fields boundary conditions (e.g. sand supply, sand availability and wind regimes; Telfer and Hesse, 2013; Ewing and Kocurek, 2010) but also monitoring dune dynamics (Hugenholtz et al., 2012; Zheng et al., 2022). Further prospects include the application of this workflow to higher resolution DEM to perform joint analysis of superimposed dunes analysis, to temporal datasets to monitor and analyze dunes dynamics with regards to wind data (e.g. ERA5-Land reanalysis data).

## CRediT authorship contribution statement

**Jimmy Daynac:** Writing – original draft, Writing – review & editing, Validation, Software, Methodology, Investigation, Formal analysis, Conceptualization. **Paul Bessin:** Writing – review & editing, Methodology, Investigation, Validation, Resources, Funding acquisition, Conceptualization. **Stéphane Pochat:** Writing – review & editing, Validation, Investigation, Formal analysis, Conceptualization. **Régis Mourgues:** Writing – review & editing, Validation, Methodology. **Samuel Shumack:** Writing – review & editing, Validation, Software.

## Declaration of competing interest

The authors declare that they have no conflict of interest.

## Data availability

Copernicus DEM – Global and European Digital Elevation Model (COP-DEM) GLO-30: https://doi.org/10.5270/ESA-c5d3d65

The QGIS data (QGIS project with outlines, crestlines, defects, and morphometric analysis) presented in the paper is available on: https://github.com/jdaynac/Aeolian-dunes-mapping-workflow

## Acknowledgment

This work was carried out as part of Jimmy Daynac's PhD thesis (2021-2024, Le Mans Université). It was supported by the Programme National de Planétologie (PNP) of CNRS- INSU cofunded by CNES (project BEDFORMAP 2022 and 2023) and by the program Mission pour les Initiatives Transverses et Interdisciplinaires (MITI) of CNES-CNRS (project CALEPAB 2022 and 2023) and also benefited from a « Encouragement » Grant of the Fondation Banque Populaire Grand Ouest (2020, P.Bessin). We thank former Master trainees Aaneesha Cunthen and Esteban Gautier, and our colleagues Edouard Ravier, Sofyane Hesni, Jean Vérité (LPG-UMR CNRS 6112, Le Mans Université), Sabrina Carpy,
Olivier Bourgeois (LPG-UMR CNRS 6112, Nantes Université), and Jean-François Buoncristiani (Biogéosciences-UMR CNRS 6282, Université de Bourgogne) for fruitful discussions about the wide scope of bedform morphological and morphometric mapping automation. We would also like to thank reviewers Matt Telfer and David M. Kennedy, who have helped improve this work considerably.

## Appendix A. Supplementary material

Supplementary data associated with this article can be found in the online version, at doi: https://doi.org/10.1016/j geomorph.2024.10 9369. These data include the Google map of the most important areas described in this article.

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