The first step is the selection of the best pairs of pre- and post-event satellite images aimed at making a change detection analysis. Nowadays, the free satellite images with the best resolution are Sentinel-2 (10 m visible and near-infrared bands) followed by Landsat ones (30 m).

We search for images and filter images using the following criteria: i.

cloud cover < 5 %;

In the second step, we calculated NDVIvar by computing the NDVI variation between the pre- and post-event conditions (Eq. 1). The aim is to identify areas with decreased NDVI values due to vegetation removal or damage caused by shallow landslides. Using the raster calculator of QGIS software, we computed the NDVI using the NIR and red band.

In the specific case of our study areas, we use the Sentinel-2 band of NIR (Band 8) and red (Band 4), which have a spatial resolution of 10 m: 1NDVIvar=NDVIpost-NDVIpre, where NDVI=(NIR-Red)/(NIR+Red). Then we manually select the NDVIvar threshold that best identifies changes related to landslides. This threshold does not have a fixed value, as reported in the literature (Hölbling et al., 2015; Mondini et al., 2011). An operator manually determines it after a visual assessment of NDVIvar, the comparison on GEE of the NDVI times series between affected and not affected areas, and the calibration of the parameters based on a PL–ML inventory comparison (back analysis). For instance, in our study areas, both the visual pattern of NDVIvar and the observation of the NDVI time series suggest that the optimal threshold should be in the range of -0.20 to -0.15, but this could be different for other cases.

In the third step, the results coming from NDVIvar are filtered using geomorphological parameters (Table 2). We first used the slope derived from DTM (downloaded from Regione Piemonte, 2011, and Regione Liguria, 2022, databases) to filter out the areas with a slope angle below a certain threshold. Also, in this case, the value is empirically based on the visual pattern and back analysis (slope distribution of ML). Specifically, to create PL, we applied this procedure: (i) the rasters of NDVIvar and slope are converted in a Boolean raster (0–1) using the thresholds mentioned above (e.g. B = [NDVIvar < -0.16 and slope > 15∘]) in a raster calculator of QGIS, where in the computed raster the value 1 corresponds to the potential shallow landslides (PLs); (ii) then on QGIS, we convert the value 1 of the raster into vectors (polygon); (iii) the median slope (always with QGIS) is calculated for each PL polygon and further filtered with a certain threshold (e.g. > 17∘); and (iv) the polygons are smoothed to obtain a more geomorphological shape. Additional filters may be introduced based on radiometric (e.g. removing the area in permanent shadow) or geometric parameters (e.g. removing the PL that overlaps with a riverbed). These filters based on empirical thresholds should be evaluated case by case, considering the morphology, the land-use data and the ancillary data available in the study area. We finally obtained the final PL inventory with its centroid.

We used the PL centroid to create with QGIS a kernel (Terrell and Scott, 1992) heatmap relative density (KD) map of relative PL. The PL KD aims to identify the most affected area. The parameters (e.g. search radius, size of the cell) used to generate KD maps depend on the dimension of the study area and the average distance of PL centroids. The same procedure is applied to the ML to create a density map for inventory comparison.

Usually, manual mapping is done on a representative training area (e.g. at least 70 % of the whole AOI) (Mondini et al., 2011; Mohan et al., 2021; Trigila et al., 2013), and it is used as a benchmark dataset for calibrating the proposed method, then it is validated on a small area (30 %). In this work, having to test a new methodology, we decided to operate through calibration and manual mapping on 100 % of the area of interest to determine if the technique is sufficiently robust.

The first PL inventory is then compared with an ML drawn on high-resolution images in a limited subarea of the AOI.

The identification of the training area is based on the following criteria: (i) the availability of cost-free high-resolution post-event images; (ii) PL density, calculated with the method described in the previous paragraph; (iii) the intensity of the event (e.g. accumulated rainfall); and (iv) the representativity of the study area in terms of land use and geomorphology. Once the result of the training area is available, it is possible to evaluate the statistical distribution of the ML inventory in terms of NDVIvar, slope angle or other parameters for a better empirical calibration of the thresholds used to create the PL. The calibration step aims to reduce false positives and false negatives and to obtain the definitive PL inventory.

Following the methodology described in Sect. 3.1, we first selected the pre- and post-event images. For our case studies, we used the data of Sentinel-2 satellites (bottom-of-atmosphere reflectance in cartographic geometry – L2A) available on the Sentinel Hub portal (Copernicus Open Access Hub, 2023). In particular, we downloaded the 10 m resolution bands visible (B2, B3, B4) and near-infrared (NIR – B8), and we clipped the original datasets on the area of interest. The datasets used in this study are listed in Table 1. For the Gavi area, we find a pair of images with a 1-year interval, while for the Tanarello and Arroscia Valley areas, the best pair of cloud-free images is on a 2-year interval.

In the second step, we defined the NDVIvar and geomorphological thresholds. In our case study, we used NDVIvar ≤ -0.15 joined to slope > 15∘ entry values to create the Boolean raster where the value 1 identifies the potential landslides. The slope models were computed from 5 m DTM available from the databases of the Piemonte and Liguria regions and were adopted to the spatial resolution of Sentinel-2 in the raster calculator of QGIS (i.e. it averages the values of four cells of 5 × 5 m into one cell of 10 × 10 m). The Boolean raster keeps the same spatial resolution as Sentinel-2 (10 × 10 m pixel).

We used additional geomorphological thresholds, such as the median slope of the PL polygons. The values were based on the statistical distribution of the ML median slope. We used the filter values' median slopes ≥ 17∘ and ≥ 20∘ for the Tanarello and Arroscia Valley areas and the Gavi area, respectively.

In the Tanarello and Arroscia Valley case, we removed the polygons nearby (using an empiric buffer from 5 to 10 m) the hydrographic network to remove false positives related to riverbank erosion. We also filtered the areas in a constant shadow because of a cliff, using threshold values of the averaged means of the four 10 m bands (RGB and NIR) of Sentinel-2 images. The PL polygons were finally smoothed and merged if their distance was lower than 1 m.

For our study, we employed a stringent calibration and validation methodology in both of our study areas, with an equal ratio of 1 : 1. This differs from the commonly used approach in the literature of a 7 : 3 ratio, as reported in studies such as Mondini et al. (2011) and Mohan et al. (2021). Our decision to utilise this methodology was motivated by the fact that it was our first time implementing this approach. Furthermore, we employed a statistical validation method that is user-friendly and straightforward to replicate in future studies.

For the Tanarello–Arroscia case, the training–validation area is about 300 km2, while it is 50 km2 for the Gavi 2019 case.

Concerning the Gavi area case study, we applied the proposed methodology as in an ordinary scenario; therefore, we performed over 10 % (about 50 km2) of the area training and validation, and then, with the previously defined parameters, we applied the method to 90 % (500 km2) of the area, producing the inventory. The large 2019 area is also intended to be used as a test inventory for other studies.

The manual mapping of the landslides was made (in early 2022) on very-high-resolution post-event images. In our case study, high-resolution images were available for both areas, dating back to a few months after the events (Table 2). We used the post-event satellite images available on Google Earth uploaded as an XYZ tile layer on QGIS software (Hafen, 2022). We also used pre-event high-resolution orthoimages available as a web map service (WMS) on the national cartographic service of Italy or the regional web map service of the Piemonte and Liguria regions.

The manual polygons of landslides (MLs) were drawn following geomorphological criteria with the help of shaded relief DTM. Two operators manually checked the inventories to reduce the subjectivity of mapping. The landslide mapping was made on QGIS with the support of Google Earth Pro for historical image visualisation.

We also use GEE's potentiality to check and compare the NDVI time series affected by shallow landslides. We manually draw some sample polygons on the GEE interface, imported as feature collections representative of different conditions (landslide/no landslides) and land use. As for the choice of the best images described in Sect. 3.1, we use code based on Nowak et al. (2021). We also extract the NDVI time series using the GEE time series explorer QGIS plugin (GEE Timeseries Explorer, 2020​​​​​​​); such script allows for producing single-pixel time series directly from a point vector. The time series analysis aims to estimate vegetation recovery in the area affected by shallow landslides and to compare it with healthy areas. The vegetation recovery helps assess the maximum period in which a post-event image can be used to calculate NDVIvar. The NDVI time series located in different land uses were also compared using GEE.

The distribution and kernel density (KD) (search radius 1000 m) of PL centroids are shown in Fig. 6a. At the basin scale, there is a high density of PL in the central sector, particularly in the Arroscia, Armetta and Tanarello valleys, where the density reaches a peak of 10 centroids km-2. Moreover, Fig. 6b shows a PL detail corresponding to riverbank erosion not filtered out because the hydrographic network has no precise high-resolution geocoding, and the derived 5 m buffer did not intersect the PL. It is challenging to create an affordable geomorphological filter discriminating river erosion from a shallow landslide in a steep valley, and in many cases, the two processing overlap or are linked by a cause–effect relationship. Figure 6c shows the correct detection of a landslide; its shape is almost accurate considering the Sentinel-2 resolution, while Fig. 6d shows a shallow landslide not detected (false negative case) because the shadow mask filters it out.

The manual mapping of landslides made on post-event Google Earth and high-resolution satellite images was compared with pre-event aerial photos of 2012 (MASE, 2012) and allowed for the detection of 1098 MLs (average density 3 ML km-2). The intersection of PL and ML datasets produced about 2620 cases.

Figure 7a shows, over a sample area, some examples of the intersection between PL and ML inventories. In Fig. 7b, the intersections are classified into the five types of combinations defined in Fig. 4​​​​​​​. In some cases, the PL–ML overlapping (TP) is almost complete (intersection 1) in Fig. 7a and b, while in others (intersection 2), TP cases represent a small portion of the intersection. For the whole Tanarello and Arroscia Valley case study, we also reported the intersection case pie charts by polygon count (Fig. 7c) and total area (Fig. 7d). It can be noted that the biggest difference between count and area statistics (25 % to 13 %) is for the FN case because it corresponds to many MLs with a small area. In contrast, FP shows a slight increase because the size of PLs is always more than 100 m2 (i.e. the Sentinel-2 spatial resolution).

Detailed validation results for PL made with R (see Sect. 3.3) are shown in Fig. 8. The chart of Fig. 8a shows the number distribution of TP, PP and FP cases. The TP represents about 32 % of intersected PL summed with the PP, representing 29 % of intersections, showing that the methodology correctly detects a shallow landslide in 60 % of cases. The area frequency distribution chart (Fig. 8b) indicates that the PP cases have smaller areas (median 165 m2) than the TP (230 m2) cases; this means that the TP increases in up to 38 % of the cases considering the area sum instead of the polygon count. Several FP cases correspond to fluvial processing like bank erosion that filters could not remove. Some other regions correspond to artificial forest cuts that occurred from 2016 to 2018. In addition, the only complete summer cloud-free pair of images is August 2016 vs. August 2018, and this extended period increased the probability of detecting land-use change not related to landslides.

The NDVIvar and the slope are the main parameters used to detect landslides; therefore, their distribution inside the intersected PL–ML inventories helped us to understand the efficiency of the semi-automatic approach. Figure 8c shows the median NDVIvar for each class of ML–PL intersections. The TP cases show NDVIvar values below the -0.16 threshold, probably because the shallow landslides strongly impact vegetation compared to other land-use changes. Figure 8d shows the median slope distribution; in this case, there are few differences among the classes because the slope filter (17∘) removed most FPs related to the slope gradient. This means that most FP cases are caused by a land-use change or riverbank erosion with the same slope gradient of shallow landslides.

The FN and PD intersection cases are discussed in Sect. 4.3.1 because they are not coming from PL and are not related to parameters used for PL methodology but to the relation of landslide size with the spatial resolution of the satellite.

Figure 10 shows the kernel centroid density (based on a search radius of 1000 m) and distributions for the PL inventory (Fig. 10a). About 3000 PLs were identified using the parameters and the filters described in the methodology section; 1100 of them are inside the training area. It can be observed that the training and validation areas show the highest PL density. Other areas of high PL density are located north of Ovada and south of Acqui Terme. Here, manual mapping on high-resolution (HR) images is proposed for further manual mapping. It is possible to analyse the different cases of PL methodology results in more detail. Figure 10b shows the correct detection of a landslide, and its shape is almost accurate considering the Sentinel-2 resolution. Figure 10c shows a PL that partly detected shallow landslides: in many cases, the trigger points are detected because of their abrupt changes, while the bottom part with more shallow sediment flow is not detected. Two small shallow landslides not caught on Sentinel-2 images are also shown. Figure 10d shows a false positive case where PL most probably detected a change in vegetation activity within a vineyard.

Also, for the Gavi area case study, we made similar statistics for the inventory intersection used for the Tanarello and Arroscia Valley case study. The manual mapping of landslides, made on post-event Google Earth, and high-resolution satellite images compared with pre-event aerial photos of 2018 (Regione Piemonte, 2020) resulted in 1178 MLs (average density 23 ML km-2). The intersection of PL and ML datasets produced about 2982 cases.

Figure 11a shows, over a sample area, some examples of the intersection of PL and ML inventories. In Fig. 11b, the intersections are classified into the five types of combinations (TP, FP, FN, PD and PP) defined in Fig. 4. In some cases, the PL–ML overlapping (TP) is almost complete (case 1) or partial (case 2). In other cases (3) the PL allowed us to detect only a tiny portion of the intersection, and most of the shallow landslide area was classified as PD. For the whole 2019 study area, we also represented the intersection case pie charts by polygon count (Fig. 11c) and area (Fig. 7d). It can be noted that in contrast to the 2016 case, there is little difference between the count by number or total areas. The different distributions of ML size (see Fig. 13b) could explain this.

Detailed validation statistics results for PL made with R (see Sect. 3.3) are shown in Fig. 12. The chart of Fig. 12a shows the number distribution of TP, PP and FP cases. The TP represents about 43 % of intersected PL summed with the PP, representing 37 % of cases, showing that the methodology correctly detects a shallow landslide in 80 % of cases. The results of semi-automatic mapping for the Gavi AOI are better than for the Arroscia–Tanarello AOI. The better performances could be explained by a better pair of pre- and post-event images and the stronger magnitude of the 2019 event. The area frequency distribution chart (Fig. 12b) shows that the partial positive cases have smaller areas (median 165 m2) than TP (230 m2); this implies that the percentage of TP rises from 43 % to 49 % of PLs considering the area sum instead of polygon count. FP cases generally correspond to changes in agriculture activity that occurred in 2019–2020 in the vineyard. As previously stated, NDVIvar and slope were analysed in terms of intersection class and provided the same insight concerning the influence of vegetation health and acclivity.

As mentioned in the Tanarello and Arroscia case study (Sect. 4.1.3), The FN and PD intersection cases are discussed in Sect. 4.3.1.

The detection capacity is mainly related to shallow landslide size and the spatial resolution of Sentinel-2.

Figure 13a and b show the histogram distribution of ML size for the Tanarello and Arroscia valleys and Gavi study areas, respectively. The ML size distribution agrees with the classical power-law distribution of shallow landslides (Bellugi et al., 2021; Guzzetti et al., 2002) for both cases studied. This means that the shallow landslides smaller than 500 m2 are about 60 % of all ML inventories, but they represent only 20 % of the total area affected. The histograms also show that for the Tanarello and Arroscia valleys (Fig. 13a), the MLs are generally smaller than in the Gavi area. The parts of the bars that are black coloured show the ML intersected by PL (TP + PD intersection cases). It is possible to note that the small landslides (100 m2) are underestimated by PL, while for large landslides, PL almost fits the ML. These results agree with the area frequency distribution for TP and PD cases shown in Figs. 8b and 12b.

Figure 13c and d show the DR calculated with Eq. (2) for the Tanarello and Arroscia valleys and Gavi study areas. The DR increases with the size of the landslides, and it is strictly related to the pixel size of Sentinel-2. For the landslides smaller than 100 m2 (Sentinel-2 spatial resolution), the DR ranges from 10 % for Tanarello and Arroscia Valley (Fig. 13c) to 15 % for the Gavi area (Fig. 13d). It is clear that for these landslides, the Sentinel-2 platform is not the optimal choice (Fiorucci et al., 2018), and manual mapping on high-resolution images is better than semi-automatic mapping. On the other hand, for the ML in the class area (500–1000, i.e. 5–10 pixels of a Sentinel-2 image), the DR ranges from 65 % for Tanarello and Arroscia Valley to 80 % for the Gavi area.

The overall DR considering polygon count is 39 % for the Tanarello and Arroscia Valley and 58 % for the Gavi case study, while considering the area sum, the DR is 60 % and 75 %, respectively. The Gavi case study's better performance is likely related to the size distribution of shallow landslides and the better pair of images used to create PL.

The performance metrics precision (P) P = TP / (TP + FP), recall R = TP / (TP + FN) and F1 score F1​​​​​​​ = 2TP / (2TP + FP + FN) without considering the intersection cases are reported in Table 3. The overall performance of our methodology is comparable with other studies, especially those using middle-resolution images (Ghorbanzadeh et al., 2021; Mondini et al., 2011; Handwerger et al., 2022). A recent study (Ganerød et al., 2023) using Sentinel-2 has shown different performances depending on the study area in Norway; the best is from the deep-learning approach with a U-net architecture. Using high-resolution Planet images (Bhuyan et al., 2023) achieves high performance over several study areas. However, we assume that the different study/training/validation settings, the image used and the event type made this comparison relative.

Both in the Tanarello and Arroscia valleys and Gavi areas do the results of spatial correlation of ML and PL density show a good agreement (Fig. 14), a further confirmation of the effectiveness of the PL methodology. Specifically, in the case of 2019, both ML and PL inventories, Fig. 14a and b, show a higher density in the northern sector of the study area and a lower density in the central region. Figure 14c shows the scatterplot between the PL and ML density; the correlation coefficient (Benesty et al., 2009) has a value of 0.85 with an R2 = 0.73 using a grid of 1000 m. Moreover, the average ML density is about 23 ML km-2 higher than the 2016 event (3.1 ML km-2). The difference is probably related to the more intense rainfall of October 2019 (up to 500 mm in 24 h) compared to the 2016 case (700 mm in 5 d).

We also manually checked Google Earth and noticed the same performance in a small validation area outside the Gavi training area.

In the case of 2016, there are more discrepancies. A higher density of PL in the NE sector (Fig. 14d) can be noted. At the same time, ML shows a density peak in the Arroscia Valley (Fig. 14e). Both datasets show that centroids' high density is located in the central sector, particularly in the Arroscia, Armetta and Tanarello valleys, where the density reaches a peak of 10 centroids km-2. At the basin scale, PL–ML regressions show a correlation coefficient of 0.68 with an R2 = 0.47 using a grid of 2500 m (Fig. 14f).

We deeply investigate the role of land use in landslide detection. The semi-automatic detection performed well for naturally vegetated slopes, while the detection capability decreased for cultivated landscapes.

For instance, the statistics on intersection cases for the four main land-use classes (Land Cover Piemonte, 2022) made for the 2019 case study allowed us to understand the variable regarding the land-use efficiency of semi-automatic mapping.

The forest and the new forested shrub areas (Fig. 15a and b) show a high percentage of TP cases, and about 80 % of PL corresponds to shallow landslides. Here, human disturbances are limited, and the majority of NDVIvar is related to landslides. The FN (15 % of the area) fits small landslides not detectable with Sentinel-2 because of its spatial resolution.

The vineyard land use (Fig. 15c) shows a high FP percentage (37 %). In this land use, most FP cases are changes related to vineyard management. FN is also higher (22 %) compared to the forested areas. The cultivated land (Fig. 15d) shows a high percentage of FN (30 %). The underestimation can be explained by smaller landslide dimensions and the agricultural practice that erases the signs of landslides.

Figure 16a and b show the NDVI time series based on Sentinel-2 computed on GEE (see “Data availability” section). The NDVI time series of the area affected by shallow landslides (red line in Fig. 16) is based on averaged NDVI of a subset of ML polygons with an area of at least 500 m2. This time series is compared with the time series averaged over a region not affected by landslides (black line in Fig. 16).

In the case of the Arroscia–Tanarello 2016 study area (Fig. 16a), it can be observed that in the areas not affected by landslides, the NDVI has a relatively constant seasonal trend during 2015–2021, ranging from 0.25 in winter to 0.75 in summer. On the contrary, the areas affected by shallow landslides showed a substantial decrease in NDVI (from 0.75 to 0.4) in the post-event 2017 summer. The NDVI slowly increased during the following years, up to the value of 0.55 in 2021. If we compare the pair images (23 August 2016, 28 August 2018​​​​​​​) used to extract the PL, we can observe an average NDVIvar of -0.2. Unfortunately, the summer 2017 images that show the best NDVIvar are not fully cloud free or are not acquired in the same seasonal period.

In the case of the Gavi case study (Fig. 16b), in those areas not affected by landslides, the NDVI has a constant seasonal trend during the period 2016–2021, ranging from 0.2 in winter to 0.8 in summer. In contrast, the NDVI of the areas affected by shallow landslides shows a substantial decrease, showing a value of 0.6 (-0.2 variation) in the 2020 summer. The NDVI value rebounded to 0.65 in 2021. The pair images (26 June 2019, 20 June 2020) used to extract the PL show an average NDVIvar of -0.15. The vegetation seems to recover faster compared to the 2016 case.

The effects of land use on detection capabilities are difficult to solve with simple filters. A partial solution could be the NDVI time series analysis. The analysis of the single-pixel time series of NDVI, generated with the GEE QGIS plugin (GEE Timeseries Explorer, 2020​​​​​​​), allowed us to better understand the effect of landslide size and land use on the capacity detection of Sentinel-2; the main results are resumed in Fig. 17.

Figure 17a and a' show the location and the comparison of two NDVI time series in a broadleaf forest land use: the 1-p is entirely inside an ML of approximately 1500 m2, while the 2-p is an undisturbed area. The two time series show almost the same seasonal trend until the 2019 event; after this, the NDVI of 1-p shows values of 0.2 less than the NDVI of 2-p in the 2020 summer.

Figure 17b and b' show the location and the comparison for two single-pixel time series located in a vineyard land use. In this case, the 5-p is situated in an ML with an approximate size of 500 m2 not detected by PL methodology (a false negative case). Both slide (5-p) and no-slide (6-p) NDVI time series show an irregular trend, probably related to the agricultural activity inside the vineyard. The post-event time series shows lower NDVI values for the pixel inside the ML; however, the noise is too high to extract a clear trend.

Figure 17c and c' show the location and NDVI time series of a false positive PL in a vineyard land use (9-p). In this case, the agricultural activity inside the vineyard caused a NDVIvar < -0.16 using the pre- and post-event pair images. However, if we look at the whole time series, there is no trace of the effect of shallow landslides.

Instead of considering single pre- (26 June 2019) and post-event (20 June 2020) dates, the noise could be reduced if we use the averaged pre- and post-event summer (May–September) images. Multi-temporal-averaged satellite data on GEE have already been used to improve landslide detection (Lindsay et al., 2022). For instance, using this approach, the FP of Fig. 17c disappears because the NDVIvar is -0.16 for single pairs, while it is -0.03 for the averaged summer periods.

The summer-averaged pre- and post-event NDVIs computed with GEE for the Gavi area are available in the “Data availability” section.