esa-sceva/satcom-chunk-collection huggingface dataset:
# Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing
## 2 System Model
### Noncoherent Detection  
The received signal \(\mathbf{r}_{k}\) at the \(N_{\text{rx}}\) BS antennas at time instant \(k\) can be written as  
\[\mathbf{r}_{k}=\mathbf{H}\mathbf{b}_{k}+\,\mathbf{n}_{k}\,, \tag{4}\]  
where \(\mathbf{H}=[\mathbf{h}_{1},\dots,\mathbf{h}_{N_{\text{rx}}}]\) is the \(N_{\text{rx}}\times N_{\text{u}}\) channel matrix collecting the complex-valued channel vectors \(\mathbf{h}_{u}\) of the users as defined in (1), \(\mathbf{b}_{k}=[b_{k,1},\dots,b_{k,N_{\text{rx}}}]^{\mathsf{T}}\) comprises the transmit symbols of each user \(u\), and \(\mathbf{n}_{k}=[n_{1,k},\dots,n_{N_{\text{rx}},k}]^{\mathsf{T}}\) gathers the circular-symmetric complex Gaussian noise \(n_{m,k}\) with zero mean and variance \(\sigma_{n}^{2}\) at the \(m\)-th receive branch. The transmit symbols are differentially encoded unit-magnitude phase-shift keying (DPSK) symbols, which are generated as follows:  
\[b_{k,u}=a_{k,u}\,b_{k-1,u}\,,\ \ \ \ \ b_{0,u}=1\,, \tag{5}\]where \(a_{k,u}\) are the data symbols drawn from an \(M\)-ary PSK constellation \(\mathcal{M}=\{\mathrm{e}^{\mathrm{j}2\pi\mathrm{i}/M}\mid i=0,1,\ldots,M-1\}\). Due to the PSK signaling, the total received power per user is \(||\mathbf{h}_{u}||_{2}^{2}\) and the signal-to-noise ratio (SNR) is given as \(||\mathbf{h}_{u}||_{2}^{2}/\sigma_{n}^{2}\).  
Assuming the channel to be constant during a transmission burst (blockfading channel), noncoherent detection of user \(u\) is performed block-wise over a temporal block \(\mathbf{R}\) of \(N_{\text{bl}}\) time steps given by  
\[\mathbf{R}=\left[\mathbf{r}_{0},\cdots,\mathbf{r}_{N_{\text{bl}}-1}\right] \tag{6}\]  
and on the basis of the \(N_{\text{bl}}\  
denotes the covariance matrix of the initial received signal \(\mathbf{r}_{k}\). The PSP \(\hat{P}_{m,u}\) (spatial per-user power) after digital beamspace preprocessing can be defined as  
\[\hat{P}_{m,u}\overset{\text{\tiny def}}{=}\text{E}\{|\mathbf{w}_{m}^{\text{H}}\mathbf{h} _{u}|^{2}\} \tag{14}\]  
and the resulting SINR of the \(u\)-th user at the \(m\)-th receive branch is given as  
\[\text{SINR}_{m,u}=\frac{\hat{P}_{m,u}}{\mathbf{w}_{m}^{\text{H}}\sigma_{\text{n}}^ {2}\mathbf{w}_{m}+\sum_{u^{\prime}\
eq u}\hat{P}_{m,v}}. \tag{15}\]  
The beamforming matrix \(\mathbf{W}_{\text{BF}}\) should be designed to maximize the SINR in (15) for the respective users and to fulfill the condition  
\[\mathbf{W}_{\text{BF}}^{\text{H}}\mathbf{W}_{\text{BF}}\approx\mathbf{I}_{N_{\text{rx}}} \tag{16}\]  
to ensure the noise to be spatially white. In the following, the composition of \(\mathbf{W}_{\text{BF}}\) is discussed for a full- and sub-array architecture.
## 4 Results
### Shear Properties of EMWM
#### 4.2.1 Effect of Shear Rate on EMWM  
Figure 17 illustrates the test results of EMWM-10 sheared at 0.2 mm/min, 2 mm/min, and 20 mm/min uniaxial unidirectional constant speed, respectively. The load at a shear rate of 20 mm/min is significantly higher than the value at 0.2 mm/min. This is due to the fact that the shear linear displacement is significantly reduced relative to the tensile, so the uniaxial tensile rate is too fast resulting in increased shear deformation, which raises the load [1]. The rapid shear rate leads to a premature straightening of the wire, which then leads to an increase in the amplitude of the load, indicating that the specimen enters the damage deformation stage (stage III) more quickly.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Level** & **1** & **2** & **3** \\ \hline \(K_{1}\) & 184.55 & 226.85 & 282.46 \\ \(K_{2}\) & 202.46 & 200.01 & 184.62 \\ \(K_{3}\) & 238.62 & 198.77 & 158.55 \\ \(R\) & 54.07 & 28.08 & 123.91 \\ \hline \end{tabular}
\end{table}
Table 10: Range analysis of shear experiments.  
Figure 17: Load–displacement curves at different rates in shear tests.
## 5 Numerical Examples
### AH-1G Rotor in Forward Flight  
The AH-1G rotor [34] in forward flight was simulated. The rotor had two blades with the optimal load survey/tip aerodynamics and acoustics test (OLS/TAAT) airfoil. The rotor radius was equal to 6.7 m, and the blade aspect ratio was 9.8 and had a linear twist from \(0^{\circ}\) to \(-10^{\circ}\) from root to tip. Each blade was modeled with 2400 panels, with 60 panels along the chordwise direction and 40 panels along the spanwise direction. The rotor was operated at an advanced ratio of 0.19, the tip mach number was equal to 0.65, and the thrust coefficient was equal to 0.00464. An azimuthal angle step of \(3^{\circ}\) was used in the present simulation.  
Figures 10 and 11 show the pressure coefficient at a span location equal to 60%\(R\) and 96%\(R\) and at azimuth angles of \(30^{\circ}\), \(90^{\circ}\), \(270^{\circ}\), and \(300^{\circ}\). Figure 12 illustrates the variation in the sectional thrust coefficient at span positions of 75%\(R\), 87%\(R\), 91%\(R\), and 97%\(R\) over one revolution. The predicted results agree reasonably well with both the experimental data and the results computed by a CFD simulation [35]. The BVI influence on the normal force was captured by the present method on the advancing side at azimuthal angle of 50-100\({}^{\circ}\) and on the retreating side around an azimuthal angle of 270\({}^{\circ}\).  
Figure 10: Pressure coefficient at \(r/R=0.60\).  
Figure 9: Pressure coefficients at a collective pitch angle of \(8^{\circ}\).  
Figure 11: Pressure coefficient at r/R = 0.91.  
Figure 12: Sectional thrust for the AH-IG rotor at different radial locations.
# A Novel Algorithm of Haze Identification Based on FY3D/MERSI-II Remote Sensing Data
## 2 Materials and Methods
### MHAM Algorithm
#### 2.3.3 Identification of Clear Conditions over Bright Surface
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Scenarios** & **Selected Areas** & **Selected Time** \\ \hline \multirow{2}{*}{**clear1**} & 42.8496\({}^{\circ}\)\(\sim\)45.3657\({}^{\circ}\), 109.1090\({}^{\circ}\)\(\sim\)113.6038\({}^{\circ}\) & 8 November 2019/4 April 2020/ \\  & 42.2122\({}^{\circ}\)\(\sim\)43.1121\({}^{\circ}\), 108.6515\({}^{\circ}\)\(\sim\)109.7193\({}^{\circ}\) & 3 December 2019 \\ \hline \multirow{4}{*}{**clear2**} & 23.9992\({}^{\circ}\)\(\sim\)24.3478\({}^{\circ}\), 112.7604\({}^{\circ}\)\(\sim\)113.6705\({}^{\circ}\) & 8 November 2019/3 December 2019 \\  & 23.0716\({}^{\circ}\)\(\sim\)23.7766\({}^{\circ}\), 115.0593\({}^{\circ}\)\(\sim\)115.8996\({}^{\circ}\) & 2 December 2019 \\  & 25.3634\({}^{\circ}\)\(\sim\)25.9159\({}^{\circ}\), 116.7444\({}^{\circ}\)\(\sim\)117.5885\({}^{\circ}\) & 15 March 2020 \\ \hline \multirow{2}{*}{**cloud1**} & 27.8471\({}^{\circ}\)\(\sim\)29.0374\({}^{\circ}\), 103.8887\({}^{\circ}\)\(\sim\)105.2329\({}^{\circ}\) & 8 November 2019/23 December 2019/ \\  & 3 April 2020/17 June 2020 \\ \hline \multirow{2}{*}{**cloud2**} & 36.1867\({}^{\circ}\)\(\sim\)36.7887\({}^{\circ}\), 108.4950\({}^{\circ}\)\(\sim\)109.3658\({}^{\circ}\) & 8 November 2019/24 December 2019/ \\  & 1 April 2020/22 June 2020 \\ \hline \multirow{2}{*}{**haze1**} & 38.0390\({}^{\circ}\)\(\sim\)39.24\({}^{\circ}\), 115.2247\({}^{\circ}\)\(\sim\)116.4105\({}^{\circ}\) & 8 November 2019/13 December 2019/ \\  & 6 April 2020/11 June 2019 \\ \hline \multirow{2}{*}{**haze2**} & 33.9950\({}^{\circ}\)\(\sim\)35.4849\({}^{\circ}\), 113.6284\({}^{\circ}\)\(\sim\)114.8294\({}^{\circ}\) & 8 November 2019/13 December 2019/ \\  & 26 April 2020/18 June 2020 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The MERSI-II data set used for training the identification condition with bright surfaces. and five clear sky conditions, the remaining pixels marked in white in Figure 7g were identified as haze pixels. Figure 6: Test of cloud detection conditions at UTC0500 on 1 December 2019. **(a)** A true color map. **(b)** The cloudy region was detected by cloud condition 1, **(c)** the cloudy region was detected by cloud condition 2, **(d)** the cloudy region was detected by cloud condition 3 **(e)** and the final cloudy regions were detected by three conditions. Figure 7: Test of clear detection conditions at UTC0605 on 3 December 2019. **(a)** A true color map. **(b)** The cloudy region was detected by three cloud conditions and the first clear condition, **(c)** the clear pixels were detected by clear condition 2, **(d)** the clear pixels were detected by clear condition 3, **(e)** the clear pixels were detected by clear condition 4, **(f)** the clear pixels were detected by clear condition 5 and **(g)** the final cloudy regions and clear pixels were detected by three cloudy conditions and five clear conditions.
## 5 Energy Detection Process
### Noise Uncertainty Estimation  
The threshold values of (14) and (15) are derived based on the knowledge of the exact noise variance \(\sigma_{n_{i}}^{2}\). However, in practice, it is very difficult to assume the exact level of noise variance in any moment. This is a consequence of the fact that the total noise can vary significantly from time to time since it consists of the noise from the receiver and environmental and thermal noise together. This noise power fluctuation, known as NU, causes a decrease in the accuracy of the sensing sensitivity. The drawback of this phenomenon is that the accuracy of detection falls quickly, which can cause SU interference in the PU [45]. Therefore, neglecting the existence of NU leads to a limitation in assessing the performance of the ED.  
To achieve a more realistic scenario, it is necessary to take into account the impact of the NU variations on the ED process. Uncertainty of noise power can be expressed by the NU factor \(\rho\) (\(\rho\geq 1\)). Therefore, the bounds of the noise variance (\(\sigma_{NU_{i}}^{2}\)) are assumed to be in the interval \(\sigma_{NU_{i}}^{2}\epsilon[\frac{\sigma_{n_{i}}^{2}}{\rho},\ \rho\sigma_{n_{i}}^{2}]\) defined by NU factor \(\rho\). The detection probability and the false alarm probability in the case of NU can be derived from (11) and (12), respectively. The expressions for detection probability and the false alarm probability are:  
\[P_{d_{i}}^{NUI}=\min_{\sigma_{NU_{i}}^{2}\epsilon[\frac{\sigma_{n_{i}}^{2}}{ \rho},\rho\sigma_{n_{i}}^{2}]}Q\left(\frac{\lambda_{i}-\left(P+\sigma_{NU_{i}}^ {2}\right)}{\sqrt{\frac{2}{N^{NU}}\left(P+\sigma_{NU_{i}}^{2}\right)}}\right)= Q\left(\frac{\lambda_{i}-\left(P+\frac{\sigma_{n_{i}}^{2}}{\rho}\right)}{\sqrt{ \frac{2}{N^{NU}}\left(P+\frac{\sigma_{n_{i}}^{2}}{\rho}\right)}}\right) \tag{19}\]\[P_{fa_{i}}^{NUI}=\max_{\sigma_{NUI_{i}}^{2}e^{\frac{\sigma_{n_{i}}^{2}}{\rho}}\rho _{n_{i}}^{2}}Q\left(\frac{\lambda_{i}-\sigma_{NUI_{i}}^{2}}{\sqrt{\frac{2}{N^{ NOT}}}\;\sigma_{NUI_{i}}^{2}}\right)=Q\left(\frac{\lambda_{i}-\rho\;\sigma_{n_{i}}^{2}}{ \sqrt{\frac{2}{N^{NOT}}\;\rho\;\sigma_{n_{i}}^{2}}}\right) \tag{20}\]  
According to relations (19) and (20), the probability of PU detection when the received signal is impacted by NU and the fixed detection threshold is:  
\[P_{d_{i}}^{NUI}=Q\left(\frac{\rho Q^{-1}\Big{(}P_{fa_{i}}^{NUI}\Big{)}-\Big{(} SNR\;-\;\frac{\rho-1}{\rho}\Big{)}\sqrt{\frac{N^{NU}}{2}}}{\frac{1}{\rho}+ SNR}\right) \tag{21}\]  
The selection of factor \(\rho=1\) implies that there is no NU and relations (19), (20) and (21) converge towards relations (11), (12) and (13), respectively. However, the case when \(\rho>1\) implies the existence of NU and the larger values of \(\rho\) mean a larger NU range. For example, when the NU factor is 1.02, it means that the variations of the noise power are 2% of the average level of received noise power.
# Improved Video Action Recognition Based on Pyramid Pooling and Dual-Stream C3D Networks
## 2 Methodology
### Classification of Movements  
#### 2.4.1 Three-Dimensional Convolutional Neural Network Variable-Scale-Based Feature Extraction  
Spatial pyramid pooling (SPP) is a widely used feature extraction method for image classification and target detection [15], which, unlike the traditional 2D convolutional methods, is capable of handling images with variable dimensions. In this study, the three-dimensional pyramid pooling (SPP) method is used and introduced into the C3D network, replacing the original maximum pooling layer, so as to optimise the spatio-temporal feature extraction of the video. The 3D pyramid pooling is performed by pooling the cubic feature maps of different sizes output from the Conv5-b layer of the C3D network, which are finally fused into a fixed-length feature vector, as shown on the left side of Figure 5.  
In 2D pyramid pooling, assuming that the last convolutional layer produces a number of future maps of different sizes and assuming 256 dimensions in the future map, for these future maps do not use the pooling operations of 4 \(\times\) 4, 2 \(\times\) 2, and 1 \(\times\) 1, and finally combined, it is guaranteed that the different sizes of future maps after the pyramid pooling are all able to produce 21 (= 4 \(\times\) 4 + 2 \(\times\) 2 + 1 \(\times\) 1) features [21].  
In this work, we accept the concept of 2D pyramid pooling and introduce it into the C3D network by adding a 3D pyramid pooling layer after Conv5-b of the C3D network to replace Pool5 in the original C3D network. The specific 3D pyramid pooling process is shown in the right half of Figure 5. Combined with the pooling kernel formula and step size  
Figure 5: Two-dimensional pyramid pooling and three-dimensional pyramid pooling.  
formula of the 2D pyramid network [22], the pooling kernel formula and step size formula of the 3D pyramid pooling are shown in Equation (15) and Equation (16), respectively:  
\[Pooling\ kernel=\left\lceil\frac{L}{pt_{i}}\right\rceil\times\left\lceil\frac{H}{ ps_{i}}\right\rceil\times\left\lceil\frac{W}{ps_{i}}\right\rceil \tag{15}\]  
\[Step\ length=\left\lceil\frac{L}{pt_{i}}\right\rceil\times\left\lceil\frac{H} {ps_{i}}\right\rceil\times\left\lceil\frac{W}{ps_{i}}\right\rceil \tag{16}\]  
where \(\rm{L}\times\rm{H}\times\rm{W}\) is the size of the cubic future map output by the C3D network Conv5-b, and \(\rm{pt_{i}}\) and \(\rm{psi}\) describe the 3D pooling level of the \(\rm{i}\)th layer of the pyramid; \(\rm{i}\in\{1,2,3\}\), \(\rm{ipt}\) is set to 1, and \(\rm{ips}\) is set to 2i.  
In summary, the whole pooling process of the 3D pyramid is equivalent to dividing the different sizes of cube future maps generated by Conv5-b of the C3D network according to the different sizes of cube grids and performing the maximum pooling operation on each small cube grid and finally fusing these features to obtain a fixed-length feature vector with the length of [1 \(\times\) (21 \(\times\) k)], which combines the C3D network of the Conv5-b output, taking a k value of 512.
## 2 Estimation of Sideslip Angle
### The Unitire Model  
During practical driving, owing to the time-variable road conditions and driving environment, the tires are under an unstable status, which complicates the modeling of tires. Thus, building a tire model that can accurately describe the real movements of tires is the basis for research on vehicle dynamics. The unitire model featured by high modeling precision, excellent theoretical boundaries, and whole working condition coverage [30; 31] was selected here and used to compute tire forces.  
The longitudinal slip rate \(S_{x}\) and lateral slip rate \(S_{y}\) of the tire model are:  
\[\left\{\begin{array}{l}S_{x}=\frac{V_{x}-R\Omega}{|R\Omega|}\\ S_{y}=\frac{V_{y}}{|R\Omega|}\end{array}\right., \tag{5}\]  
where \(V_{x}\) is the longitudinal velocity at the center of a tire; \(V_{y}\) is the lateral velocity at the center of the tire; \(R\) is the valid rolling radius of the tire; \(\Omega\) is its rotating speed.  
The relative longitudinal slip rate \(\Phi_{x}\), relative lateral slip rate \(\Phi_{y}\), and relative total slip rate \(\Phi\) of a tire are:  
\[\left\{\begin{array}{l}\Phi_{x}=\frac{K_{x}S_{x}}{H_{x}F_{z}}\\ \Phi_{y}=\frac{K_{y}S_{y}}{H_{y}F_{z}}\\ \Phi=\sqrt{\Phi_{x}^{2}+\Phi_{y}^{2}}\end{array}\right., \tag{6}\]  
where \(F_{z}\) is the vertical loading of a tire; \(\mu_{x}\) and \(\mu_{y}\) are the longitudinal friction factor and lateral friction factor; \(K_{x}\) and \(K_{y}\) are the longitudinal rigidity and lateral rigidity.  
The longitudinal force \(F_{x}\), lateral force \(F_{y}\), and aligning torque \(M_{z}\) of the tire are:  
\[\left\{\begin{array}{l}F_{x}=\overline{F}_{x}\mu_{x}F_{z}\\ =\mu_{x}F_{z}\bullet\left[1-\exp\left(-\[PERSON]_{1}\[PERSON]^{2}-\left(E_{1}^{2}+ \frac{1}{12}\right)\[PERSON]^{3}\right)\right]\bullet\frac{\[PERSON]_{x}}{\[PERSON]}\\ F_{y}=\overline{F}_{y}\mu_{y}F_{z}\\ =\mu_{y}F_{z}\bullet\left[1-\exp\left(-\[PERSON]_{1}\[PERSON]^{2}-\left(E_{1}^{2}+ \frac{1}{12}\right)\[PERSON]^{3}\right)\right]\bullet\frac{\[PERSON]_{y}}{\[PERSON]}\\ M_{z}=F_{y}D_{x}\\ =F_{y}\left[\left(D_{x0}+D_{e}\right)\exp\left(-D_{1}\Phi-D_{2}\Phi^{2}\right) -D_{e}\right]\end{array}\right., \tag{7}\]  
where \(\overline{F}_{x}\) and \(\overline{F}_{y}\) are the dimensionless longitudinal force and lateral force; \(E_{1}\) is the longitudinal curvature factor or lateral curvature factor; \(D_{x}\) is the aligning force arm;\(D_{x0}\), \(D_{e}\), \(D_{1}\), and \(D_{2}\) are the structural parameters of \(D_{x}\). The main parameters of the Unitire model are listed in Appendix A.
# Enhancing Communication Security in Drones Using QRNG in Frequency Hopping Spread Spectrum
## 5 Implementation  
To implement true random frequency hopping in communication systems, several critical components and processes must be established. This section describes the practical implementation, including the setup of the Randomness Processing Unit (RPU), the generation and synchronization of frequency hopping sequences, and the security protocols necessary to maintain the integrity and confidentiality of the communication.
# Microbial Biopolymers: From Production to Environmental Applications--A Review
## 6 Applications of Microbial Biopolymers
### Microbial Biopolymers as Adsorbents
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Polymer** & **Pollutant** &
\begin{tabular}{c} **Adsorption** \\ **Capacity** \\ **(mg g\({}^{-1}\))** \\ \end{tabular} & **References** \\ \hline \multicolumn{4}{c}{Inorganic contaminants} \\ Carboxylated cellulose nanocrystal/sodium alginate hydrogel & Pb\({}^{2+}\) & 335.3 & [278] \\  & Cu\({}^{2+}\) & 80.12 & \\  & Cd\({}^{2+}\) & 102.23 & \\ Cellulose/PVA/Graphene Composite aerogel & Cr\({}^{2+}\) & 123.02 & \\  & Co\({}^{2+}\) & 62.38 & \\  & Zn\({}^{2+}\) & 69.55 & \\  & Pb\({}^{2+}\) & 57.16 & \\ Thioglycolic Acid-Esterified Cellulose Nanocrystals & Cu\({}^{2+}\) & 4.244 & [280] \\ Chitosan-glucose hydrogel & Co\({}^{2+}\) & 202 & [281] \\ Chitosan/orange peel hydrogel & Cu\({}^{2+}\) & 116.6 & \\  & Cr\({}^{6+}\) & 107.5 & \\  & Cu\({}^{2+}\) & 115.1 & \\ Xanthate-modified chitosan/poly (N-isopropylacrylamide) & Pb\({}^{2+}\) & 172.0 & [283] \\  & Ni\({}^{2+}\) & 66.9 & \\ Cellulose/guar gum/biochar & Cu\({}^{2+}\) & 805.45 & [284] \\ Cellulose/bentonite grafted polyacrylic acid hydrogel & Cd\({}^{2+}\) & 242.53 & [285] \\  & Alginate/polyethyleneimine & Cu\({}^{2+}\) & 322.6 & \\  & Pb\({}^{2+}\) & 344.8 & [269] \\
3D network nanostructured sodium alginate & Cd\({}^{2+}\) & 9.54 & \\  & Cu\({}^{2+}\) & 13.38 & [286] \\ \hline \multicolumn{4}{c}{Hyaluronic acid-supported magnetic microspheres} & Cu\({}^{2+}\) & 12.2 & [287] \\ Xanthan gum/n-acetyl cysteine modified mica biom nanocomposite & Cu\({}^{2+}\) & 177.2 & [288] \\  & Ni\({}^{2+}\) & 51.48 & \\ Poly (Acrylamide-co-Acrylic Acid)/Xanthan Gum hydrogel & Cd\({}^{2+}\) & 312.15 & \\  & Ni\({}^{2+}\) & 185.0 & [289] \\ Pullulan/polydopamine hydrogels & Cu\({}^{2+}\) & 100.9 & [290] \\ Sodium alginate/coffee waste & Pb\({}^{2+}\) & 984.4 & [291] \\ Whey protein concentrate/pullulan hydrogel & Cu\({}^{2+}\) & 81.6 & [292] \\ Polylactic acid hydrogel & Pb\({}^{2+}\) & 416.07 & \\  & Ni\({}^{2+}\) & 243.10 & [293] \\ \multicolumn{4}{c}{Organic contaminants} \\ Sodium hydroxide activated acrolein/chitosan & Acid blue 93 & 2500 & [294] \\  & Direct blue & 534.25 & \\ Carboxymethyl cellulose/chitosan/triethyleneenetramine & Congo red & 519.53 & [295] \\ Cellulose/guar gum/biochar & Methylene blue & 598.28 & [284] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Studies related to the use of biopolymers as adsorbents to treat wastewater.
## 3 Data Collection and Elaboration
### Gully Erosion Inventory  
The inventory of the spatial distribution of gullies is fundamental data for mapping gully erosion susceptibility because it represents the dependent variable in the prediction models. In this work, the inventory map of gully erosion landforms was realised using the visual interpretation of orthophotos, dating 2008 (1:5000 scale) and downloaded by the website of the Cartographic Center of Calabria region ([[http://geoportale.regione.calabria.it/opendata](http://geoportale.regione.calabria.it/opendata)]([http://geoportale.regione.calabria.it/opendata](http://geoportale.regione.calabria.it/opendata)), accessed on 30 November 2020), and Google Earth images available from 2010 to 2022. In addition, field investigations were carried out using a GPS receiver device to localise the gullies' position. The field survey highlighted that gully erosion processes are mainly active in areas with sparse or no vegetation cover, as well as in arable lands and grasslands. Several ephemeral gullies were observed on croplands, mainly during intense rainfall events due to water runoff concentration. These processes cause a severe soil loss (Figure 2a). Permanent gullies with steep and bare walls, indicating an active stage of dissection, were mapped on hillslopes where sand and conglomerate deposits crop out (Figure 2b). In addition, a dense network of gullies often dissects clayey slopes. Within the catchment, a total of 529 areas involved in gully erosion processes were recognised. The gully areas were mapped in polygon format and, successively, each polygon was transformed to a point representing the centroid of the head-cut area of the gullies (Figure 1b).