*2.5. Satellite–Derived Topography: Photogrammetry Reconstruction*

Three couples of panchromatic images, which were characterized by three intersection angles, were processed using the opensource software RSP (RPC stereo processor, [15], Figure 5) from the tri–stereo images from Pleiades–1. RSP was used to process stereo satellite images so as to create point dense clouds and then to create a Digital Surface Model (DSM) using the photogrammetry technique. For each pair of images, RSP used the Rational Polynomial Coefficients (RPC) files, which were delivered with the Pleiades–1 images, which contain the geometric parameters for the same images to build the projection

relationship between the 3D and 2D space. The additional Ground Control Points (GCP) increased the accuracy of the reconstruction horizontally and vertically.

**Class Name Thumbnail** Dune Salt marsh Rock Urban Forest Field Beach Road Seawater

**Table 2.** Pleiades–1 natural–coloured thumbnail of the nine coastal landscape classes.

Three image pairs (1) without, (2) with 1, or (3) with 3 GCP (DSM#2–3\_0, DSM#2–3\_1, DSM#2–3\_3, DSM#1–2\_0, DSM#1–2\_1, DSM#1–2\_3, DSM#1–3\_0, DSM#1–3\_1, DSM#1–3\_3) were computed using RSP, and nine DSM were evaluated using the root mean square error (RMSE). The lowest RMSE was the factor that identified what the best photogrammetry– based DSM was.

$$RMSE = \sqrt{\frac{\sum\_{i=1}^{n} (Pi - Oi)^2}{n}},\tag{1}$$

where *P* is the value of the calculated DSM ellipsoidal height; *O* is the value of the LiDAR ellipsoidal height; and *n* is the number of observations.

**Figure 5.** Flowchart describing methodology for coastal landscape classification from Pleiades– derived topography and morphometry.

In addition, the DSMs were also evaluated at the ecosystem scale by referring to the nine identified classes. A mean of the ellipsoidal heights per class was calculated, and a dispersion parameter such as standard deviation was determined to show the homogeneity or heterogeneity of the statistical series.

The MS images underwent three pre–processing stages before they were integrated into the analyses:

ENVI's FLAASH tool was used to correct the influence of the atmosphere (top of atmosphere, TOA) for each pixel in the images. The radiometric correction of the MS images consisted of converting the numerical radiance values into TOA reflectance values. The reflectance was calculated according to the radiance/irradiance (solar) ratio.

The MS images were also geometrically corrected using both the RPC files and the DSMs, which had been created previously from the panchromatic stereo images. This pre– processing stage corrected the distortions in the images that were related to the positioning of the satellite or the structure of the landform.

The MS images were pan–sharpened using the Gram–Schmidt algorithm. It resampled the 2 m pixel size of the MS image to be of the 0.5 m pixel size of the panchromatic images (see James et al., 2021).

#### *2.6. Satellite–Derived Morphometry*

The morphometric features such as slope, aspect, topographic position index (TPI), and TPI–based landform classification (TPILC) were calculated from the best DSMs using the SAGA GIS opensource software (Figure 5) [16]. These indicators that were related to the topography of the study site were coupled with the basic RGB spectral information to reveal the contributions of each predictor. The near–infrared band of the image was also compared to the morphometric predictors.

The slope highlights the inclination of a pixel, and this aspect defines the orientation of the slope from a compass direction. The slope and aspect predictors generate raster images that are computed from the DSM. The percentage of slope is the ratio between the difference in altitude and the horizontal distance. A 3 × 3 pixel moving window compares the values of a pixel around its neighbors to define the slope percentage.

TPI computes the elevation or altitude of each pixel and subtracts it from the mean elevation or altitude of a neighborhood of that pixel of a grid raster [17]. Values that are lower than 0 correspond to valleys. Values higher than 0 are ridges, and those that are around 0 are flat areas. TPI–based landform classification was founded on the same principle as the basic TPI. Two different scales were combined to allow for the better identification of the topographic differences [18].

### *2.7. Classification Algorithm*

A supervised machine learning classifier algorithm was tested: maximum likelihood (ML) with ENVI® software (Figure 5) [19]. ML is a probabilistic method that calculates the variance and covariance of each class by assuming that the statistics of each class in each band are normally distributed. A pixel is then assigned to the class with the most likely probability of membership.

An array of 500 calibration pixels and 500 validation pixels per class were extracted from the satellite–derived products (Table 2). Overall accuracy (OA) is determined as the sum of the correctly classified pixels divided by the number of pixels. The producer accuracy (PA) corresponds to the accuracy of the map from the producer's point of view, i.e., from the algorithm. The result expressed in % indicates the fraction of correctly classified pixels of those that are known to belong to the class [20]. The OA of each by–product combination was evaluated through the calibration/validation pixels that were calculated with the confusion matrix.

#### **3. Results**

After the DSMs were derived and evaluated, the best one was further investigated to build topographic by–products. A ML algorithm was applied to this DSM using nine representative landscape classes from the study site. The contribution of each derived topographic band was evaluated at the landscape (OA) and class (PA) level.

#### *3.1. Pleiades–1 Digital Surface Model*

#### 3.1.1. Global Evaluation

The results of the overall DSM evaluation showed a slight increase in the overall accuracy of the DSMs with the addition of GCPs (Figure 6). Thus, without GCP, with 1 GCP, and with 3 GCPs, the results were 4.03 m, 4 m, and 4.01 m for DSM#2–3 (Figures 6 and 7a). DSM#1–2 and DSM#1–3 increased their accuracy by 0.04 m and 0.02 m, respectively, as soon as a GCP was added (Figures 6 and 7b,c). However, image pairs #1–#2 and #1–#3 gave unsatisfactory results compared to image pair #2–#3.

**Figure 6.** Bar plot of the root mean square error from Pleiades–1 DSM computed by pairs without, with 1, or with 3 ground control points.

At the global scale, the analysis of the three best DSMs (DSM#2–3\_1, DSM#1–2\_3, and DSM#1–3\_3) can be compared to the validation points that were extracted from the LiDAR– 2018 (Figure 7a–c). The distribution of the DSM#2–3\_1 points shows a low dispersion and therefore a positive correlation between the LiDAR–2018 dataset and DSM#2–3\_1 (Figure 7a). The DSM#1–3\_3 appeared to be sparsely correlated to the LiDAR–2018 dataset.

#### 3.1.2. Class Level DSM Evaluation

The analysis of the DSM results from the Pleiades–1 images can also be examined at the class level (Figure 8) on the sub–study site. Based on the validation polygons from the classes, each DSM was evaluated.

**Figure 7.** *Cont*.

**Figure 7.** Comparison of ellipsoidal height of the LiDAR dataset and the three best digital surface models: DSM#2–3\_1 (**a**), DSM#1–2\_3 (**b**) and DSM#1–3\_3 (**c**).

**Figure 8.** Ellipsoidal mean and standard deviation height at the class level on the sub–study site from the three best digital surface models.

Depending on the ecosystem, the mean heights between the DSMs within the same class can vary. This is the case for almost all of the classes if the three DSMs are compared to each other.

However, when DSM#2–3\_1 and DSM#1–3\_3 are compared to each other (due to their performance at the landscape scale), the mean differences in heights were: +10.35 m, +10.22 m, +13.16 m, +15.24 m, +15.11 m, +13.95 m, +10.83 m, +7.71, and +6.15 m for the salt marsh, dune, rock, urban, forest, beach, road, and seawater classes, respectively.