Keywords

1 Introduction

Landslides are significant natural hazards that cause damage to human settlements and their economic activities, especially in mountainous areas where abrupt relief, rainfall and/or earthquakes trigger gravitational processes (Sim et al. 2022). Worldwide, geomorphological cartography is used as a valuable tool to assess the landslide susceptibility. It provides concrete and precise information of distribution, frequency, size, origin, and chronological sequences of landslides (Jasiewicz and Stepinski 2013). The elaboration of geomorphologic maps requires high quality materials, such as topographic cartography, aerial photographs, and digital terrain models to analyze the landscape and its relationship with geological, structural, lithological, tectonic, morphometric, morphographic, weathering, and human factors (Knight et al. 2011). At regional scale, these materials are obtained by satellite and aerial remote sensing techniques that use multispectral sensors, LiDAR, synthetic aperture radars (SAR), and digital cameras (Francioni et al. 2018).

However, at local scale the geomorphologic evaluation of landslide processes is difficult not only because the small-scale cartography, but also due to other natural and technical problems. The complexity concomitant of these natural and technical problems affects and compromises the landslide susceptibility assessment (Haneberg 2005). To mitigate these problems, intensive fieldwork improves landslide data collection, as well as knowledge of an area, but does not guarantee an exhaustive representation of gravitational processes (Van Den Eeckhaut et al. 2005). Also, its application is limited when researchers want to monitor short-term changes in an area due to the costs and effort required. To solve this situation, high spatial and temporal resolution aerial photos and DTMs are essential for the interpretation, detection, measurement, and modeling of small landslides.

In recent years, with the advent of Unmanned Aerial Vehicles (UAVs), or drones, and their products (aerial photos, orthophotos, dispersed or dense point clouds, and Digital Elevation Models (DEM)) a new opportunity has emerged to satisfy researcher needs (Annis et al. 2020). However, because this technology relatively new, there is still no robust methodology for acquiring and processing images derived from UAVs. The methodology depends highly on the used software, and has a significant influence on the resulting accuracy (Colomina and Molina 2014). For example, the DEMs derived from the UAVs do not separate the different return levels of the laser detection and measurement signals as does LiDAR. Therefore, UAVs produce Digital Surface Models (DSM) with a zenith vision in which the surface corresponds to the elements present on the earth’s surface (vegetation, buildings, cars, etc.) and locally, if no obstacle, to the ground. In contrast, LiDAR, by separating the different return levels of the laser detection and measurement signals, allows both creation of DSM and Digital Terrain Models (DTM, to virtually represent terrain topography without artifacts) (Dubbini et al. 2016). Limitations of DSM derived from the UAVs to create a DTM are partially resolved during post-processing that eliminates other elements not corresponding to ground data (called “noise”) by using specialized photogrammetry programs (Dubbini et al. 2016).

Governmental and academic institutions use commercial programs specialized in photogrammetric processes to eliminate the noise and to produce high-resolution DSMs and DTMs. DTMs are obtained by post-processing the DSM semi-automatically or automatically. The semi-automatically procedure eliminates the noise by manually enclosing and erased with selection polygons vegetation, buildings, cars, etc. The program then interpolates the ground elevation to fill the gaps left by the elimination of the noise to produce the DTM. For an automatic procedure, the user defines the best parameters (such as angles, distances, minimum heights from which a point must not be considered as a ground, the average slope of the terrain, concavity, etc.) to reclassify the elevation point cloud in two classes (points representing the ground, and the remainder) (Anderson and Gaston 2013; Dubbini et al. 2016; Escobar-Villanueva et al. 2017).

Although the use of this new technologies is Mexico is very promising as a tool for the rapid acquisition of aerial photos, orthophotos, and 3D data to map and assess remote landslide areas, there is a lack of non-commercial programs and methods to facilitate post-processing of point cloud datasets from UAVs to produce DTM at low cost, and in an acceptable manner. Also, little work has been done to obtain the landslide susceptibility in areas with difficult access and scarce or small-scale cartographic and geomorphologic information.

The present study develops algorithms, applications, and an alternative method to eliminate the existing noise in an UAV-derived DSM which allow an adequate DTM (referred as a moderate-resolution DTM) to be obtained for landslide susceptibility evaluation. The method uses a 50 cm-pixel resolution DSM derived from an UAV, a DTM derived from a map with 10 m topographic contour lines (referred herein as low-resolution DTM), a Canopy Height Model (CHM), altimetric selection mask, interpolation, weights, and a low-pass filter to obtain a 50 cm moderate-resolution DTM.

The moderate-resolution DTM is the foundation to assess the landslide susceptibility by using Multiple Logistic Regression (MLR) in the study area. The study area is the Cerro de la Miel, in the Municipality of Tepoztlán, State of Morelos, Mexico (Fig. 1). In the area, rockfalls and shallow landslides were triggered by an Earthquake (magnitude 7.1) on September 19, 2017 and are used to evaluate the method and its landslide susceptibility. In this study, MLR is selected to assess landslide susceptibility because it avoids problems of non-linear relationships between dependent and independent variables. Also, MLR landslide probability prediction is fairly successful in identifying current and potential landslide areas (Field 2014; Legorreta et al. 2016; Castro-Miguel et al. 2022). Three topographic variables derived from the moderate-resolution DTM (altimetry, slope, and terrain curvature) are used as the input for MLR analysis. The results illustrate that although the moderate-resolution DTM shows a vertical error of ~ <=1.5 m, the method allows elimination of much of the DSM inherent noise. The resulting DTM has a fair topographic representation that permits calculation of the landslide susceptibility. The calculated landslide susceptibility has a moderate match between the inventory map and the model (76.91%). The landslide model validation is performed by the model’s accuracies obtained from a cross table between models and landslide inventory and with the Receiver Operating Characteristic (ROC) curve.

Fig. 1
A three-dimensional piece of land that represents Mexico, from which a square piece of land is extracted and presented separately.

Study area, Cerro de la Miel, Tepoztlán, State of Morelos, Mexico

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2 Study Area

The Cerro de la Miel is at 18° 59′ 13.920″-18° 59′ 20.1048″ N and 99° 6′ 45.2889″-99° 6′ 38.7957″ W, within the municipality of Tepoztlán, State of Morelos, Mexico (Fig. 1). The study area belongs to the Tepoztlán Formation, which is composed of reworked volcanoclastic deposits caused by mud flows or lahars (Lenhardt et al. 2010). The Cerro de la Miel is affected sporadically, but importantly, by gravitational processes. Rockfall and shallow landslides are triggered constantly due to the combination of several factors, such as high precipitation, land use changes caused by human settlements, a high degree of weathered bedrock located at high elevations with steep slopes, and earthquakes.

The study area covers 3.63 ha with an elevation range from 1789 to 1875 m a.s.l., and hillslopes from 3° to 35° (in the piedmont zone) and > 35° (in mountainous terrain). The deposits of the Tepoztlán Formation contain angular and subangular dacitic clasts 20 cm to >2 m in diameter. These clasts vary in resistance from strong (rock specimens are broken with a single hammer stroke) to weak (the rock specimens are fragmented under firm a hammer stroke) (Dackombe and Gardiner 1983). These clasts are bound in a matrix composed of silt and sand.

The instability situation is exacerbated by an heterogeneous sets of fractures, predominantly vertical and with a NE-SW trend. These fractures allow the infiltration of water, which in turn creates alteration planes that weaken the contact between the blocks and facilitates their fall. The average annual rainfall is 1592 mm/year. Most of the rain fall occurs as seasonal storms during the wet season between May and November (CLICOM 2018). Access to the upper part is difficult due to the abundant low deciduous forest vegetation (CONANP 2017).

On September 19 2017, at 13:14:40 local time, an intense earthquake with a magnitude of 7.1 on the Momentum Magnitude (Mw) scale struck the country. The epicenter was located 12 km from Axochiapan (Morelos), according to the preliminary special report of the National Seismological Service of Mexico (Servicio Sismológico Nacional 2017). This earthquake generated an estimated economic loss between US $ 4000 and US $ 8000 million (Capraro et al. 2018). During this seismic event, a rock fragment of approximately 3.1 m long × 2.8 wide × 1.7 m high detached from a height of 57 m. The rock impacted a house located on the SW flank of the Cerro de la Miel, but not human lost were reported.

3 Method

The method encompasses four main stages to obtain a moderate-resolution DTM, and for modeling, mapping, and validating landslide susceptibility in the study area. Stage 1: Planning, fieldwork, and post-processing of products derived from a UAV to obtain a high-resolution DSM (50 cm pixel size) (stage 1 in Fig. 2); Stage 2: Obtaining and standardizing a DTM derived from altimetric curves (stage 2, Fig. 2); Stage 3: Obtaining the canopy height model and altimetric mask to create the final moderate-resolution DTM by using weights and filters (stage 3, Fig. 2), and Stage 4: Create the landslide susceptibility map and assess the performance of the MLR model (stage 4, Fig. 2).

Fig. 2
A flow chart consists of the following stages, 1. Process to obtain a high resolution D S M, 2. Obtaining and standardizing a low resolution D T M, 3. Obtaining the moderate-resolution D T M and 4. Mapping landslide susceptibility and evaluation of model efficiency.

General method to obtain a DTM and the landslide susceptibility

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Although the first stage described how the ASCII or LAS (Long ASCII Standard) file was obtained with X, Y, and Z coordinates in this research, the focus of this work is the post-processing of the ASCII or LAS file, regardless the photogrammetric process or programs used (for example, Argisoft PhotoScan, Pix4D, VisualSFM, Accute3D, etc.) to obtain them.

For the first stage, used a Phantom 4 Pro quadrocopter, designed and built by Da-Jiang Innovation (DJI) with a camera with CMOS sensor of 1″ providing 20 megapixels of resolution. The flight capture planning was carried out using the Pix4D capture program (Pix4D 2022). With a photogrammetric double-mesh flight capture pattern, 103 aerial images were acquired with two flights, approximately 20 minutes in duration. The average height of the flights was approximately 100 m, and at a speed of 1.5 m/s. The front and lateral overlap between each aerial photograph was 80%.

Along with the flight planning, some ground control points (GPCs) were defined in the area to georeference the aerial photographs. Unfortunately, a large part of the study area was private property, and was difficult to access. Therefore, to help with the georeferencing process, four GPC were captured using a geodetic dual frequency differential GPS. To palliate this, Google Earth images were used to establish a large number of control points, and to georeference the images. The horizontal coordinates were referenced to the UTM 14 N zone using the WGS84 ellipsoid.

Image post-processing was accomplished using the photogrammetric software Argisoft PhotoScan (Agisoft 2014). Post-processing included alignment of aerial photographs, creating an orthophoto, and generating a dense point cloud with X, Y, and Z values. The dense point cloud was exported as an ASCII X, Y, and Z file, from which a standard high-resolution DSM was generated by using the dem_lidar_generation program (Parrot 2011). A resolution of 50 cm per pixel is established. Furthermore, a DTM of the area was obtained from the Instituto Nacional de Geografía y Estadística (Fig. 3a) (INEGI 1998a). However, it was not suitable for topographic representation and landslide susceptibility analysis due to its low resolution (15 m per pixel). As a result, in the second stage, the derivation of a more suitable low-resolution DTM was obtained from a topographic map at a scale 1:50,000 by using altimetric curves with a 10 m equidistance (INEGI 1998b). From each altimetric curve’s node, the X, Y, and Z values were extracted. Due to the sparse distribution of contour lines in the study area, the nodes were interpolated by a multidirectional linear interpolation (Parrot 2012; Parrot 2016; Šiljeg et al. 2019) (Fig. 3b and c). A low-resolution DTM of 50 cm resolution was generated for the two subsequent stages (Fig. 3d).

Fig. 3
Four contour maps that describe the procedure to obtain a D T M from a low resolution map.

Procedure to obtain a DTM from a low-resolution map: (a) 15 m resolution DTM; (b) 10 m equidistance altimetric contour lines; (c) extraction of points with X, Y, and Z from the nodes of altimetric contour lines; (d) interpolated low-resolution DTM (50 cm in pixel size)

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In the third stage, the moderate-resolution DTM was created by using the software Select Slices (Parrot 2018a), and the developed program Shaving (Parrot 2018b). The software Select Slices allows the user to create a CHM and derive binary images to use as masks that correspond to height difference of various vegetation, representing the vertical distance between the ground and the top of trees. With Shaving, templated vegetation height ranges were used to perform analyses. The CHM was created with a pixel size of 50 cm by subtracting the low-resolution DTM (derived from topographic curves) from the high-resolution DSM (derived from the UAV).

The different masks of vegetation created by the Shaving program were used to remove the noise according to vegetation height by applying a selective subtraction. Height differences were subtracted only from the area framed within the mask to the DSM. Figure 4, shows the results obtained using three different masks. One mask with noise heights ranges from 10 m to 25 m (Fig. 4d, g, j), another with heights from 10 cm to 25 m (Fig. 4e, h, k), and the last one from 0 m to 25 m (Fig. 4f, i, l).

Fig. 4
Two-dimensional and three-dimensional spatial maps that represent the results obtained using three different masks. One mask with noise heights ranges from 10 meters to 25 meters, another with heights from 10 centimeters to 25 meters, and the last one from 0 meter to 25 meters.

Example of using Select Slices and Shaving programs (a) DSM derived from the UAV; (b) DTM derived from a topographic 1: 50,000 map; (c) CHM created from the algebraic subtraction of (a, b; d) Altimetric mask (in white color) from 10 m to 25 m; (e) Altimetric mask (in white color) from 10 cm to 25 m; (f) Altimetric mask (in white color) from 0 m to 25 m; (g, h, i, j, k, l) Resulting DTMs

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This last mask was selected and used to obtain the pre-final moderate-resolution DTM. With the selected mask, the Shaving program (Parrot 2018b) was used to eliminate full ranges of height differences. If the low-resolution DTM was used to subtract the full ranges of height differences, the resulting map would have the same spatial characteristics as the low-resolution DTM, and the potential advantages obtained with the UAV are lost (Fig. 4f, i, l). To reduce this problem, we proceeded in an heuristic way.

First, the distribution of height differences in the CHM was evaluated with a histogram and then weighted. In this study, the height differences were weighted by 4%. For example, if there were in a pixel with a height difference of 5 m, by weighted 4%, the Shaving program would subtract 4.80 m rather than of 5 m. The resulting DTM still presented altimetric jumps (Fig. 5), for that, a low-pass filter was applied to obtain the final moderate-resolution DTM. With this procedure, a maximum error was estimated for the study area between 0 and 1.5 m.

Fig. 5
Two D T Ms, the first with no contour lines and the other with contour lines representing altimetric jumps.

(a) pre-weighted and filtered DTM; (b) Final weighted and filtered moderate-resolution DTM

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In the fourth stage, slope angles and slope curvature were derived from the final moderate-resolution DTM. These two independent variables together with the altimetric elevation were used to feed the MLR model for landslide susceptibility assessment. The probability of landslide triggering was calculated by use of a random sample from non-landslide and landslide areas for the three independent variables. The landslide analysis excluded evacuation zones and deposits. The total number of landslide pixels on the landslide inventory was 96 pixels (24 m2). The landslide area included the head scarps of shallow slides and rockfalls. The same number of sampled pixels (96 pixels) was sampled in non-landslide areas. With the total number of sampled pixels, the three independent variables were tested for multi-collinearity using the Variance Inflation Factor (VIF) (Pallant 2013). The VIF values in Table 1 shows no serious multicollinearity problem (Field 2014). However, the analysis of backward Multiple Logistic Regression discarded slope curvature. Based on the logit form, landslide susceptibility was mapped using a 10-classification probability scheme in the GIS (Table 1, Fig. 7a).

Table 1 Coefficients, logit form, and statistical test of MLR
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To evaluate the model prediction, LOGISNET under ArcInfo GIS software (Legorreta and Bursik 2008), and the Statistical Package for the Social Sciences (SPSS) were used. The gauge of how well the model predicted reality was assessed by the percentage of overlay between the model map and inventory map (Table 2). In LOGISNET, a two-classification scheme (landslide and non-landslide) was used for the inventory and model maps to facilitate the comparison in a contingency table. The contingency table was used to summarize the error and success in landslide and non-landslide area (overall accuracy), the degree of coincidence between the model and inventory (producer’s accuracy), the degree of model over-prediction or under-prediction, and model efficiency (user’s accuracy and model efficiency). In SPSS, the model accuracy was evaluated with the area under the ROC curve (AUC) (Legorreta et al. 2016). When the model predicted all correctly, the statistics derived from the contingency table and the AUC had a maximum value of 1 or 100%. Model efficiency went from 1 (a perfect model) to negative values when the number of pixels incorrectly indicated landslides were larger than the correct ones (Legorreta et al. 2016).

Table 2 ROC, accuracies, and model efficiency
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4 Results

Following the September 2017 assessment of triggers was included in the landslide inventory for Cerro de la Miel (Fig. 6). The landslide inventory shows that in the study area, small shallow landslides (including debris slides and debris flows) are, by number, the predominant type (23), followed rockfalls (7). They affect an area of 244.73 m2. About 78% of the shallow landslides are located along the piedmont with slopes between 8–35°, while rockfalls are the predominant process along the contact between the relative flat hilltops and hillslopes >35°.

Fig. 6
An aerial photograph of a rockfall triggered by an earthquake from the landslide inventory for Cerro de la Miel. The inventory shows that in the study area, small shallow landslides including debris slides and debris flows are predominant followed by rockfalls. The corridor and deposit have blocks ranging from small cobbles to large boulder.

(a) Landslide inventory map; (b) Rock fall detachment zone; (c) House destroyed by a ~ 15 m2 bold

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Although there is a relatively small number of large rockfalls, these are the main hazard in the study area. For example, Fig. 6 shows a rockfall triggered by the Earthquake. The corridor and deposit have blocks ranging from small cobbles to large boulders ~15 m3 in volume. The blocks were channelized toward the house by a structural fracture. Based on in situ observations, the detached rock block lost support during the Earthquake by the formation of a shallow landslide at its base.

Landslide susceptibility assessment is not suitable with a low resolution DTM for small areas and, or with unprocessed high-resolution UAV-created DSM. With our method, most landscape elements are considered as non-relevant information, or noise and are eliminated to obtain a fair topographic (bare earth) representation (Fig. 5). The processed moderate-resolution DTM is suitable for modeling landslide susceptibility with MLR. The landslide susceptibility map is categorized into 10 and 2 probability zones for description and evaluation purposes (Fig. 7). The model shows moderate coincidence with observations in the inventory and from the field. The heads of larger triggered boulders are located in non-landslide predicted zones (with probability values between 4.7 to 5). However, shallow landslides at the base of these large boulders were triggered by the Earthquake. High potential probability (>80%) of fall areas are located on the cemented flows of conglomerates with steep walls >35°. In the field it was not possible to detect landslides triggered by the Earthquake in these areas. However, some neighbors have reported damage to their properties by detachments from this wall during the rainy season.

Fig. 7
Two landslide susceptibility maps are categorized into 10 and 2 probability zones are present. The heads of larger triggered boulders are located in non-landslide predicted zones, with probability values between 4.7 to 5. High potential probability greater than 80% of fall areas are located on the cemented flows of conglomerates with steep walls greater than 35 degrees.

(a) MLR model with a ten-classification scheme. (b) MLR model with a two-classification scheme used for inventory vs. model comparison

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The AUC and overall accuracy (Table 2), also shows moderate performance of the models by using only altimetry and slope variables. The Producer’s accuracy shows that the models have >76% of coincidence with the landslide inventory map. The model tends to under-predict as it shows the moderate percentage (>66%) of user’s accuracy and low value in the model efficiency.

5 Conclusions

Landslide susceptibility is difficult to model due to the continuous changes in the topography by landslides, land use changes, and environmental conditions in remote volcanic areas with difficult access. Mapping and modeling landslide susceptibility are not suitable with a low-resolution DTM and/or with unprocessed high-resolution DSM created from a UAV. This is because the former has a poor spatial and temporal landslide representation in the topography, while and the latter includes not only the ground topography, but also other landscape elements considered as noise.

This study briefly presents a method that allows landslide specialist and other applier and users to obtain a moderate-resolution DTM from which landslide susceptibility can be evaluated. The implementation of this method at Cerro de la Miel in Tepoztlán is an attempt to produce a standardized procedure for landslide susceptibility studies in the volcanic areas of Mexico that lack high-resolution topographic information. Our method uses and adapts a governmental low-resolution DTM and a high-resolution DSM created from a UAV to obtain the moderate-resolution DSM for landslide modeling.

We emphasize that the starting point for the method is a non-pre-processing ASCII or LAS file, independent of any photogrammetric program treatment. We also acknowledge the technical limitation of using a low-resolution DTM. When a low-resolution DTM is used as a reference for the initial topography, compensations using an heuristic approach (employing mask selections, weights, and filters) are needed to eliminate most of the noise. In this research, a trade-off between a maximum topography vertical error of ~1.5 m and the selected mask, 4% of weighted, and the use of a low-pass filter was acceptable to model landslide susceptibility.

Landslide susceptibility was modeled by using three topographic variables in MLR model. The model was able to have a moderate success of landslide prediction using only slope and altimetry variables. It will be possible to improve the model if other thematic variables are used. However, in Mexico coverage of those thematic variables are temporally and spatially poor in many remote areas.

Despite these limitations, the programs developed, and analysis presented in this work are the basis of an integral methodology to obtain a UAV-derived DTM, and for slope instability prognosis.