dataesr/scientific-paragraphs-categorization huggingface dataset:
Registration of the datasets and the registration error estimate To detect geomorphic changes and landslides, the two datasets need to be co-registered as closely as possible, and any large-scale tectonic deformation needs to be corrected. The registration error to be used in Eq. (2) must also be estimated. First, a preliminary quality control is performed to evaluate the intra-survey registration quality of each dataset. This is feasible if the individual flight lines can be isolated using, for instance, the pointID information specific to each line and provided in the LAS file format. The intra-survey registration quality can be investigated with 3D-M3C2 measurements of overlapping flight lines using a 1 m regular grid of core points, from which we define the registration bias and error as the mean and standard deviation of the 3D-M3C2 distances, respectively.
The point cloud of the pre-EQ dataset results from 12 flight lines that have overlaps ranging from 60 % to 90 % (Fig. S1  in the Supplement), whereas the post-EQ point cloud corresponds to 5 flight lines with an overlap of 50 %. For each dataset, no significant bias with respect to registration is measured between lines (maximum of 3 cm for the pre-EQ survey and 1 cm for the post-EQ survey; Table  S1  in the Supplement), but the registration error ranges from 13  to 20 cm for the pre-EQ survey, and is typically around 6 cm for the post-EQ survey, with one pair of overlapping flight lines having a registration error of 12 cm. Hence, the internal registration quality of the pre-EQ dataset is significantly worse than the post-EQ dataset, a likely consequence of differences in instrument precision and post-processing methods.
Second, the registration between the two surveys must be evaluated and generally improved. As delivered, the lidar datasets have a vertical shift of between 1 and 2 m relative to each other. To correct for this shift, a grid of core points is first created by rasterizing the dataset with the largest point density -here the post-EQ dataset -with a 1 m grid spacing. A vertical-M3C2 calculation is then performed, and the mode of the resulting distribution is used to adjust the two datasets by a vertical shift of 1. 36 m. This approach is only valid when the fraction of the surface affected by landsliding is small. A subsequent 3D-M3C2 calculation is performed to obtain a preliminary map of geomorphic change. At this stage, a visual inspection of the pre-EQ and post-EQ orthoimages and of the preliminary 3D-M3C2 distances allows us to determine that there is no significant internal tectonic displacement.
The mean 3D-M3C2 distance on stable areas is -0. 01 m, showing that there is almost no bias left in the registration, and the standard deviation of 3D-M3C2 distances is 0. 17 m (Fig. 4b ). At this stage, the two datasets are considered optimally registered for the stable areas but with an unknown registration error reg. We propose defining reg as the maximum of the standard deviation of the intra-survey and inter-survey 3D-M3C2 distances in Eq. (  2 ). In the ideal case of two very high-quality lidar datasets, reg would be equal to the inter-survey registration error. In the studied case, the pre-EQ intra-survey registration error is locally worse (0. 2 m) than the inter-survey registration error (0. 17 m). Thus, we set reg = 0. 2 m, which is consistent with an estimate of reg that would be based on the combined lidar accuracy derived from GCP assuming complete correlation of errors (see Sect.
To construct the final landslide inventory, we apply the following steps: 1. labeling of at least 60 % of the provisional source inventory as actual landslide sources and false detections; 2. evaluation of the classification potential of various filtering metrics; 3. determination of the optimal filtering metrics based on a classification performance index; 4. application of the optimal filtering metrics to classify the provisional landslide source inventory in predicted landslides and predicted false detections. As the pre-EQ lidar data quality (point density and classification) is significantly worse in forests than in forestfree areas, we carry out step 2 and 3 for provisional landslide sources located in forested and forest-free areas separately. Forest areas are defined based on the number of laser returns of the post-EQ dataset (Fig.
Definition of filtering metrics As false detections mainly emerge from the errors in the data in relation to the amplitude of a real topographic change that we aim to capture, we first choose to analyze three metrics based on the 3D-M3C2 calculation: (1) the maximum 3D distance, (2) the mean LoD 95 % and (3) the mean signal-tonoise ratio (SNR). We expect the maximum 3D distance to https://doi. org/10. 5194/esurf-9-1013-2021 Earth Surf. Dynam. , 9, 1013-1044, 2021 discriminate between deep actual landslide sources and lowamplitude false detections arising from flight-line misalignments and residual registration errors characteristic of false detections in forest-free areas (Fig. 5b ). As the LoD 95 % is a direct measure of the quality of the data (point density and roughness), classification errors of vegetation should be characterized by a significantly higher mean LoD 95 % than actual landslide sources.
The SNR is defined as the ratio between the 3D-M3C2 distance and the associated LoD 95 % for each core point. This measure can be used as a confidence metric for each source. We also choose to take advantage of the ability of the 3D differencing approach to detect deposit areas to analyze the closest deposit distance (CDD). The CDD is defined for each provisional source as the closest downslope distance to a provisional deposit along the flow path using a D8 (deterministic eight-node) algorithm  (Fairfield and Leymarie, 1991). This distance is calculated from the post-EQ DEM with the MATLAB-based TopoToolbox software  (Schwanghart and Scherler, 2014). Metrics with the best potential are then tested to determine an optimal configuration of filtering metrics that best remove false detections while retaining the maximum number of actual landslide sources.
10a ). The detection errors are predominantly in bare-rock areas (116, 46 % of detection errors) and other land covers (87, 35 % of detection errors) where the prevalence of false detections in the 3D-PcD dataset is expected to be extremely low (1. 5 %); thus, the missing landslides in the 2D inventory are not potential false detections. The missed landslides can be very large landslides occurring within pronounced shadows in the post-EQ orthoimage, where the topographic change is mostly vertical (Fig. 10c ). Missed landslides also occur in forested Earth Surf. Dynam. , 9, 1013-1044, 2021 https://doi. org/10. 5194/esurf-9-1013-2021 areas, although with a lower proportion (48, 19 % of detection errors); however, we could expect from the classification of the labeled data that a third of these missing landslides may be false detection of the 3D inventory.
Vertical versus 3D change detection capability, and the M3C2 algorithm The importance of detecting changes in three dimensions (3D-M3C2), as opposed to vertically (vertical-M3C2), on steep slopes can be illustrated by an SSDS test applied to the post-EQ point cloud (Fig. 12 ). Typical of change measurement methods on rough surfaces with random point sampling (e. g. ,  Lague et al. , 2013) , a nonzero mean distance is often measured, even though the two point clouds are samples of exactly the same surface. The distribution of measured distances is centered near zero, with means of -2 × 10 -4 and 1 × 10 -4 m for the vertical and 3D approaches, respectively. https://doi. org/10. 5194/esurf-9-1013-2021 Earth Surf. Dynam. , 9, 1013-1044, 2021   5. Fits correspond to least squares fitting of a power law to log-binned data above a manually selected cutoff.
Registration and elevation errors A critical aspect of the comparison of 3D point clouds is their co-registration, in particular in the context of coseismic landsliding. In this study, a rigid transformation is applied to the datasets using an ICP algorithm  (Besl and McKay, 1992) , assuming that internal deformation induced by the earthquake is negligible. The 3D-M3C2 map does not exhibit any systematic horizontal shift north nor south of the Hope Fault. Thus, we conclude that internal deformation, if there was any, was below the typical registration error in our study area. For larger studied regions with internal deformation and in the absence of a 3D coseismic deformation model that could be applied to the post-EQ point cloud (e. g. ,  Massey et al. , 2020) , our workflow should be applied in a piecewise manner with boundaries corresponding to the main identified faults or deformation zones.
For landslide inventories following climatic events, the application to large datasets should be straightforward, as no significant internal deformation is expected. However, we note internal flight-line height mismatches of 0. 13-0. 20 m in the pre-EQ survey that are diffi-cult to correct after data delivery and generate some apparent large-scale, low-amplitude topographic changes (Fig. 4 , Table  S1  and Sect. S2 in the Supplement). Interestingly, in the M3C2 calculation, flight-line mismatches are averaged out in the distance measurement but lead to a higher local point cloud standard deviation and, thus, to an increase in the LoD 95 % and to a lower probability of incorrect topographic change detection. Despite significant flight-line mismatches in the pre-EQ dataset, using the SNR and CDD filtering approach efficiently removes the false detection source areas related to this issue in non-forested area.
Landslide segmentation The connected component segmentation is a simple, objective and rapid way to separate landslides in 3D that can be scaled up to much larger datasets. However, given the complexity of the 3D data, in particular the very large range of landslide sizes (i. e. , 4 orders of magnitude in the studied case), it inevitably exhibits some drawbacks and is subject to improvement. In particular, landslide amalgamation occurs between two sources or deposits if two of their core points are closer than D m (2 m in this study). Hence, landslides occurring on the two sides of a collapsed divide can be erroneously connected. This is the case for the largest landslide in our database which is located on the rock cliffs in the western part of the study area  (Figs. 10a, 13a). In this example, the landslide source could reasonably be segmented into at least five smaller landslides.
However, there does not seem to be a unique way to segment such a complex set of amalgamated events, even manually, underlining that landslide segmentation cannot currently be fully objective. As we aim to apply our workflow to very large datasets, potentially with several tens of thousands of landslides, and as false detection filtering needs to operate on segmented patches, automatic segmentation is a mandatory step. We have explored the use of fast implementations of a density-based spatial clustering algorithm derived from DBSCAN  (Ester et al. , 1996) , which is an algorithm used for the segmentation of 3D point clouds of rockfalls and the removal of noisy points (e. g. ,  Benjamin et al. , 2020; Tonini and Abellan, 2014 ; details in Sect. S2). We applied OPTICS (Ordering Points To Identify the Clustering Structure;  Ankerst et al.
, 1999) , recently used for rockfall segmentation of 3D lidar data  (Carrea et al. , 2021) , and HDBSCAN (Hierarchical Density-Based Spatial Clustering of Applications with Noise;  McInnes et al. , 2017) , which has a better ability to detect clusters of various sizes compared with DBSCAN and is also much faster. However, none of these approaches managed to provide a significantly better segmentation of the largest landslides of our database, and the density probability of the source area that they produce is very similar to the one generated by a connected component approach. These approaches are, however, significantly longer to run than a connected component approach in CloudCompare (Sect. S2), and they have parameters which are less intuitive to set than D m , which is a distance directly comparable to core point spacing.
New segmentation approaches accounting for normal direction, divide organization and 3D depth maps of amalgamated sources are needed to improve the segmentation of complex cases. Manual segmentation can also be envisioned as a refinement after the predicted true landslide sources and deposits have been produced, but it is irreproducible and time-consuming when applied to very large datasets. We note, however, that segmentation issues do not affect the total landslide volume calculation in our study and that a sensitivity analysis of the impact of D m shows that landslide source statistics are not severely affected by this parameter as long as it is close to the value that we have used (see Sect. 5. 2).
Landslide volume calculation Landslide volume is computed using vertical-M3C2 on regular core points. This facilitates volume calculation on potentially complex 2D landslide geometry but may lead to incorrect volume estimates on very steep slopes. However, the median slope of the source core points (measured on the pre-EQ surface; Fig. S6 ) is 33. 9 • , and only 1. 2 % of the core points have slopes higher than 60 •. Thus, we expect this effect to impact a very small fraction of our inventory. Measuring landslide volume in 3D would be preferable -for instance, along a constant surface normal direction defined for each source or deposits, but such a simple approach is not better than a vertical measurement for the complex surface geometry of large landslides observed in the dataset that are properly segmented (e.
This low value may also reflect the criteria used to label the provisional source inventory, but the value of 18 m that we obtain in forest-free area is much lower than our manual labeling criteria (30 m). While the thresholds that we derive for CDD and SNR are optimal for this region, manual labeling of a fraction of the provisional data may still be needed to evaluate the optimal threshold values in other regions and for other data registration and quality. It should be emphasized that the pre-EQ lidar data that we use probably represent a worst-case scenario for topographic change detection for two reasons. First, it has relatively large https://doi. org/10. 5194/esurf-9-1013-2021 Earth Surf. Dynam. , 9, 1013-1044, 2021 internal geometrical errors compared with a typical modern dataset, such as the post-EQ data, which translates into a poor registration error and limits our ability to detect change at ∼ 40 cm.
Our study area was chosen based on lidar data availability and contains a particularly high proportion of underdetected landslides in the 2D inventory due to the presence of actively eroding bare-bedrock hillslopes. We expect this proportion to significantly vary when considering other landscapes with potentially varying proportions of vegetation cover, vegetation density and type (e. g. , grass, shrubs, trees), lithology, and ground shaking intensity. Nonetheless, our finding represents a first approach to the issue of considering the under-detection of landslides in total landslide volume estimates. We show that extreme caution should be used when dealing with coseismic volumes estimated on landscapes where large fractions of bare-rock surfaces and sparse vegetation cover are present before an earthquake, such as the Kaikōura Ranges.
Dynam. , 9, 1013-1044, 2021 density of the pre-earthquake lidar data (Table  1 ). Considering both forested and forest-free areas, false detections only represent 0. 44 % of the total volume of the predicted inventory. Thus, the uncertainty with respect to volume is mainly controlled by the M3C2 distance uncertainty rather than the presence of false detections. Within these uncertainties, the total volumes of sources (724 297 ± 141 087 m 3 ) and deposits (954 029 ± 159 188 m 3 ) are not statistically different. The larger volume of deposits is, however, consistent with rock decompaction during landsliding, which could be constrained using a joint gravity survey in future studies  (Mouyen et al. , 2020).
10 (N LT = 29 557;  Massey et al. , 2020, Fig. 11a ) for which the power-law scaling is expressed for A > 500 m 2. A sensitivity analysis of the impact of the workflow parameters (Fig. 14 ), in particular D m which affects the level of amalgamation in the dataset, does not yield values of c smaller than -1. 67 and cannot reconcile our results with those of  Massey et al. (2020). Either our limited study area overemphasizes, by chance, the occurrence of large landslides generating a smaller value of c or the manual inventory of  Massey et al. (2020)  may miss a large fraction of intermediate and small landslides, especially on bare-rock hillslopes which are frequent in the high mountains of the Kaikōura Ranges. Most importantly, the landslide area distribution that we derive does not exhibit a rollover classically observed in 2D landslide inventories.
The probability distribution of rockfall volume generally obeys a power-law relationship with an exponent e R ranging from -1 to -2. 2 (e. g. ,  Malamud et al. , 2004; Benjamin et al. , 2020)  without a rollover. If we restrict existing inventories to those with at least 500 rockfalls and the largest rockfall of at least of 20 m 3 , the range of exponent e R narrows to -1. 5 to -2 https://doi. org/10. 5194/esurf-9-1013-2021 Earth Surf. Dynam. , 9, 1013-1044, 2021 with a majority of inventories around -1. 6 ± 0. 1  (Benjamin et al. , 2020) , which is very close to our scaling exponent. Although, we do not expect rockfalls to be a dominant mechanism in our database given the lack of very steep slopes and given that rupture mechanisms (e. g. , fragmentation, sliding, slumping), rock heterogeneity and topographic constraints (e.
g. , hillslope size) are not expected to be similar  (Dussauge et al. , 2003) , the consistency of the exponent that we find is striking. This may suggest a much larger range of scales over which the volume of landslides, encompassing rockfalls in this definition, obeys a unique scaling behavior. Datasets specifically acquired to bridge the gap between large-scale airborne lidar and terrestrial lidar are needed to get a better handle on the volume distribution of landslides, critical information with respect to risk analysis and landslide erosion calculation.
We provide various tests and recipes to estimate the registration error and to choose the parameters of the M3C2 algorithm as functions of the point cloud density to ensure the lowest level of change detection as well as the best resolution of the 3D map of change. Applied to a 5 km 2 area located in the Kaikōura region in New Zealand with pre-and post-earthquake lidar, we generate the first automatic inventory of landslide sources and deposits based on repeat 3D airborne lidar data. We show the following: -A minimum level of 3D change detection at 95 % confidence of 0. 40 m can be reached with airborne lidar data, which is largely set by the registration error. In our case, the limited quality of flight-line alignment of the pre-EQ data was the dominant source of registration uncertainty.
Nevertheless, we recommend systematically performing a 3D-PcD approach where repeat lidar data exist. This is critically needed to improve landslide science and manage the cascade of hazards following large earthquakes or storm events, by automatically identifying landslide deposits and subtle features such as subsidence developing around landslides missed in 2D inventories. Current bottlenecks to apply this workflow over larger scales, beyond the availability of high-quality 3D data, are the registration of pre-and post-EQ data when complex coseismic deformation patterns occur and the limitations of the segmentation method in high-landslide-density areas. While airborne lidar is best suited to vegetated environments and currently results in the best precision (compared with aerial or spatial photogrammetry), the workflow operates for any kind of 3D data.
Figure1. Maps of the regional context and location of the study area: (a) regional map of Kaikōura with the location of the 2016 M w 7. 8 earthquake, associated active faults and the study area; orthoimages focused on the study area dated before (b) and after (c) the earthquake with the 5 km 2 lidar dataset extent used in this paper (all images are available at https://canterburymaps. govt. nz/about/feedback/ (last access: 18 July 2021); Aerial Surveys, 2017).
Acknowledgements. We are grateful to  Alex Densmore  and  David Milledge  for the critical review that helped to improve this paper. We also wish to thank the editors,  Giulia Sofia  and  Niel Hovius , for their time and feedback. Finally, we wish to acknowledge the  European Reasearch Council , the  Agence National de la Recherche , the Brittany region and the lidar topobathymetric platform of  Rennes University  for their financial support. Financial support. This research has been supported by the  European Research Council ,  H2020 Research and Innovation program  (grant no. FEASIBLe, 803721); the  Agence Nationale de la Recherche  (grant no. ANR-14-CE33-0005 ); and the  LIDAREAU  project , Brittany region  (grant no. 2020-701 ). Review statement. This paper was edited by  Giulia Sofia  and reviewed by  Alexander Densmore  and  Dave Milledge.
Code availability. The code used to produce the landslide inventory in this study is available as a Jupyter Notebook at https: //github. com/Thomas-Brd/3D_landslide_detection (Bernard, 2021 , https://doi. org/10. 5281/zenodo. 5220611, Bernard and Steer, 2021). Data availability. The landslide source and deposit information supporting the findings of this paper can be found at https://doi. org/10. 5281/zenodo. 5113770 (Bernard et al. , 2021). Supplement. The supplement related to this article is available online at: https://doi. org/10. 5194/esurf-9-1013-2021-supplement.
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