Robert Emberson
email: robert.a.emberson@nasa.gov

Dalia B Kirschbaum

Pukar Amatya

Hakan Tanyas

Odin Marc

Insights from the topographic characteristics of a large global catalog of rainfall-induced landslide event inventories

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The impact of natural hazards on population and infrastructure is most acute where the footprints of these hazards intersect the locations where people live and buildings are situated. For some hazards like earthquakes and cyclones, the footprints of the hazard can be distributed across wide regions, but for other hazards like landslides the footprint may be significantly more localized. Landslides triggered by intense rainfall or seismic activity, however, can be distributed more broadly, the extent of which often mirrors the extent of the intense rainfall and seismic shaking [START_REF] Marc | Prediction of the area affected by earthquake-induced landsliding based on seismological parameters[END_REF], 2018, Tanyas and Lombardo 2019].

The individual landslides triggered during these extreme events occur in specific parts of the landscape that are most susceptible to failure. These slopes become critically unstable due to both preconditioning factors like slope and internal frictional strength, as well as triggering factors like change in fluid pore pressure or seismic acceleration. Landslide inventories are the ideal data source not only to better understand the spatial, temporal and size distribution of landslides but also to conduct more accurate susceptibility, hazard and risk assessments [START_REF] Guzzetti | Landslide inventory maps: New tools for an old problem[END_REF]]. Overall, landslide inventories are categorized as historical and event inventories [START_REF] Malamud | Landslide inventories and their statistical properties[END_REF]. Historical landslide inventories include many landslide events over time in a given region. Landslide-event inventories, on the other hand, contain landslides triggered by a specific trigger (e.g., earthquake, rainfall or snowmelt) of known date. In other words, the time of landslide occurrence is unknown in historical landslide inventories and therefore, for instance, landslide susceptibility models developed based on historical inventories are time-invariant products solely representing geomorphologically landslide-prone hillslopes [START_REF] Lombardo | Chrono-validation of near-real-time landslide susceptibility models via plug-in statistical simulations[END_REF]. Historic inventories are by definition biased toward frequent, climatic triggers, and are not representative of the long-term average susceptibility to triggers including earthquakes. Whereas, landslide-event inventories are more suitable data sources to develop near-real time products to predict spatial distribution of landslides triggered by a specific event [e.g., Nowicki Jessee et al. 2018].

For specific, large triggering events such as an earthquake or an episode of extreme rainfall, it is possible to relatively accurately define the timing of the event, and if high resolution imagery is found that brackets the dates in question it is also possible to systematically map the landslides generated by such a trigger [START_REF] Guzzetti | Landslide inventory maps: New tools for an old problem[END_REF]. Mapping landslides following extreme events has become common, and inventories exist for a large number of earthquakes [START_REF] Tanyas | Presentation and Analysis of Earthquake-Induced Landslide Inventories[END_REF]. A smaller number of intense rainfall events have also been mapped [START_REF] Marc | Initial insights from a global database of rainfallinduced landslide inventories: the weak influence of slope and strong influence of total storm rainfall[END_REF], but unlike for earthquakes [Schmitt et al. 2017] https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

no centralized repository of these data exists at present. Location data for landslides triggered by intense rainfall is vitally important to calibrate and validate existing susceptibility models, since the datasets produced are generally considered to be nearly complete. It is also useful to characterize the rainfall required to trigger landslides, and thus help inform local and global hazard models [Emberson et al. 2021[START_REF] Kirschbaum | Satellite-Based Assessment of Rainfall-Triggered Landslide Hazard for Situational Awareness[END_REF]. These can then be used to inform exposure and risk assessment estimates [Emberson et al. 2020].

It is important to note that the positions where earthquake-triggered landslides occur on a given hillslope are not necessarily applicable to rainfall-triggered landslides. As shown by previous research [Densmore andHovius 2000, Meunier et al. 2008], the higher peak ground acceleration in earthquakes at the top of ridges tends to increase landslides in those locations, while increasing water saturation at the base of slopes by intense rain tends to increase landslides lower down the slope [e.g., Rault et al. 2018]. As such, it is imperative to use the appropriate type of landslide inventory to calibrate any model.

In this study, we combine 10 existing inventories of landslides triggered by intense rain storms with 6 new inventories mapped using high resolution data for this study. Assessing these landslide-event inventories both individually and in combination, we assess the local topographic characteristics that are most strongly related to where landslides initiate, as well as local forest loss that can be calculated from satellite data. We suggest that these inventories and the associated parameters can be used to calibrate and validate other models of susceptibility and hazard, and will provide valuable information to authors seeking landslide data with high spatial accuracy, as well as supporting characterization of rainfall thresholds for landslide impacts [e.g. [START_REF] Conrad | A New Code for Automated Objective Optimization of Hydrometeorological Thresholds for Landslide Initiation[END_REF]. These inventories will be available on the NASA Landslide Viewer app (landslides.nasa.gov/viewer) for open access by other researchers.

Context & Methods

Landslide Inventories

It has become common practice to map areas affected by landslide-triggering earthquakes to build a spatially complete picture of landslide impacts [START_REF] Tanyas | Presentation and Analysis of Earthquake-Induced Landslide Inventories[END_REF], and the inventories that are generated have been used to produce hazard maps [START_REF] Jibson | A method for producing digital probabilistic seismic landslide hazard maps[END_REF][START_REF] Harp | Landslide inventories: The essential part of seismic landslide hazard analyses[END_REF], susceptibility models [Garcia-Rodriguez et al. 2008[START_REF] Xu | GIS-based support vector machine modeling of earthquake-triggered landslide susceptibility in the Jianjiang River watershed[END_REF], guidelines for hazard zonation [START_REF] Milledge | Simple rules to minimise exposure to coseismic landslide hazard[END_REF]] and global alerting systems [START_REF] Nowicki | A Global Empirical Model for Near-Real-Time Assessment of Seismically Induced Landslides[END_REF]]. Landslide-event inventories are also required to explore the landscape response to tectonic and climatic forcings [e.g., [START_REF] Malamud | Landslide inventories and their statistical properties[END_REF], Korup et al. 2012[START_REF] Marc | A seismologically consistent expression for the total area and volume of earthquake-triggered landsliding[END_REF], 2019]. Mapping of landslides in the aftermath of major rainfall events is somewhat less common, since cloud cover is often a significant impediment in the impacted areas, which may limit clear views from satellites. However, an increasing number of intense rainfall events have now had landslides mapped, with extensive examples in Taiwan [START_REF] Lin | Landslides triggered by the 7 August 2009 Typhoon Morakot in southern Taiwan[END_REF][START_REF] Chen | Quantifying rainfall controls on catchment-scale landslide erosion in Taiwan[END_REF], Japan and Brazil [START_REF] Marc | Initial insights from a global database of rainfallinduced landslide inventories: the weak influence of slope and strong influence of total storm rainfall[END_REF]] and the Caribbean [van Westen & Zhang 2018].

Several methods exist to generate event-specific landslide inventories. The robustness and accuracy of the final inventory depends on the type and quality of imagery and data available, as well as the method chosen. Synthetic Aperture Radar (SAR) data has been employed to generate inventories of slow-moving landslides [START_REF] Handwerger | Widespread Initiation, Reactivation , and Acceleration of Landslides in the Northern California Coast Ranges due to Extreme Rainfall[END_REF], Bekaert et al. 2020], to focus on the kinematics of single slow-moving slides [START_REF] Hu | Thickness, and Hydraulic Diffusivity of the Slow -Moving Monroe Landslide in California Revealed by L -Band Satellite Radar Interferometry[END_REF] aftermath of major triggering events [Mondini 2017, Handwerger et al. 2019, Adriano et al. 2020, Burrows et al., 2020, Jung & Yun 2020]. The most widely used technique is to map landslides directly from optical imagery, either from Unmanned Aerial Vehicle (UAV) imagery [START_REF] Casagli | UAV and ground-based remote sensing techniques for landslide mapping , monitoring and early warning[END_REF], Rossi et al. 2018], aerial photography [START_REF] Harp | Hazard Analysis of Landslides Triggered by Typhoon Chata'an on July 2[END_REF]] or satellite observations [START_REF] Casagli | UAV and ground-based remote sensing techniques for landslide mapping , monitoring and early warning[END_REF][START_REF] Martha | Object-oriented analysis of multi-temporal panchromatic images for creation of historical landslide inventories[END_REF][START_REF] Behling | Robust automated image co-registration of optical multi-sensor time series data: Database generation for multi-temporal landslide detection[END_REF]]. While satellite observations generally have the lowest spatial resolution and may be impinged by cloud cover, these satellites offer near global coverage and frequent return intervals that generally allows for imagery that brackets the event in question. This is particularly the case for some of the newer commercial satellite constellations. Some rainfall triggered events may occur in locations where cloud cover is so prevalent that it precludes anything other than seasonal assessment of landslide occurrence, such as the Himalayas during the monsoon. However, an increasing number of satellite-generated inventories now exist. The methods used to delineate landslides from optical imagery include manual mapping, where a human determines what is and is not a landslide, or semiautomatic/automatic mapping, where detection algorithms are used to determine landslide locations.

Methodology

Summarising various previous work, five mapping criteria appear essential for landslide inventories (see [START_REF] Guzzetti | Landslide inventory maps: New tools for an old problem[END_REF][START_REF] Marc | Amalgamation in landslide maps: effects and automatic detection[END_REF][START_REF] Tanyas | Presentation and Analysis of Earthquake-Induced Landslide Inventories[END_REF]: (i) manual mapping (or correction) to reduce errors and avoid amalgamation, (ii) high enough imagery resolution for completeness and to avoid amalgamation, (iii) mapping landslides as polygons to allow maximum scientific usage (e.g., area affected, volume of sediment mobilized, frequency-size distributions), (iv) mapping with pre and post-event imagery to focus on landslides with a known trigger, and (v) defined mapping boundary to clarify inventory completeness. For the purposes of this study, we have tried to obtain as many inventories as possible for comparison, while generally satisfying these five essential criteria. Nevertheless, due to varying imagery and mapping techniques, criteria (i) and

(ii) are fulfilled with variable quality for the studied inventories (Table 1). More detailed inventories have differentiated the source and deposit areas of landslides, but this often requires field validation. The locations of the inventories are shown in Figure 1.

As such, we incorporate 10 existing inventories and supplement them with 6 further inventories that we have produced for this study. The details for each of the inventories are described in Table 1. For several of the newly produced inventories, we have utilized high resolution imagery from Planet Dove satellites [Planet Team, 2017] available through the Commercial Smallsat Data Acquisition (CSDA) Program (https://earthdata.nasa.gov/esds/csdap). Planet imagery represents an important step change for landslide mapping procedures, since the high spatial resolution of approximately 3m of the images is combined with rapid return time for the satellites (of the order of 1 image per day).

For several of the newly generated inventories, we have mapped the landslides manually using GIS software. This resulted in three inventories; two in the Philippines, and one in Thrissur, India. The remaining new inventories were generated using the semi-automatic object-based methods of [START_REF] Amatya | Use of very high-resolution optical data for landslide mapping and susceptibility analysis along the Karnali highway, Nepal[END_REF]2021]. Since algorithmic methods are known to produce artifacts when broadly applied [START_REF] Pawluszek | Sensitivity analysis of automatic landslide mapping : numerical experiments towards the best solution[END_REF]] and can lead to amalgamation of individual landslides into larger polygons [START_REF] Marc | Amalgamation in landslide maps: effects and automatic detection[END_REF], each of the automatically generated inventories was additionally corrected by manual https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License. comparison with pre-and post-event high-resolution imagery in GIS software. We therefore consider each of the newly generated inventories to be of comparable quality to one another. Beyond the five essential mapping criteria, additional criteria include the differentiation of scar and deposit and the classifications of landslides according to their type/mechanisms. However, these criteria are difficult to fulfill for large event inventories (see in [START_REF] Tanyas | Presentation and Analysis of Earthquake-Induced Landslide Inventories[END_REF], especially when based on various sources of optical imagery limiting our ability to differentiate between scar and deposit areas [START_REF] Casagli | UAV and ground-based remote sensing techniques for landslide mapping , monitoring and early warning[END_REF]. 145 The mapped inventories combine scars and deposit in the polygon delineation, although in the analysis discussed below we have sought to differentiate these areas. In terms of landslide type we could not systematically classify each landslide polygon.

However, we have removed debris flows from the analysis where possible by removing long-runout landslide polygons from each mapped inventory. In general, this mapping identifies rockslides, rock avalanches, shallow soil toppling and slumping failures, but does not capture slow moving landslides where surface changes may be less evident. A focus on these kinds of landslide is warranted since the volume of material mobilized during large storms from such landslides can lead to damaging debris flows and bedload transport impacts [START_REF] Badoux | Damage costs due to bedload transport processes in Switzerland[END_REF]. Removing debris flows from the analysis allows us to provide consistent landslide maps that can be used to estimate volumes, for example using global scaling relationships like those defined by Larsen et al. [2010].

We contrast each of the inventories mapped here by comparing the size-frequency distributions of each dataset, shown in Figure 2. For each of the inventories, we show the probability of a landslide within a given area interval, as a way to assess the frequency of small and large landslides across the different datasets.

Each of these landslide events was triggered by extreme rainfall, and although it is not our intention to examine the triggering rainfall in detail in this study it is useful to briefly discuss the characteristics of the rainfall events in question. A detailed analysis of the triggering rainfall associated with several of these inventories is described by Marc et al. 2018, who used local gauge data to characterize the rainfall intensities. We were unable to find consistent local gauge data for several of the more recent events that are published here for the first time (events in Zimbabwe, Burundi, Kenya, and the two events in the Philippines). We can still use satellite rainfall data as a consistent source of rainfall for each of the events, however. To assess these, we utilize the reprocessed IMERG (Integrated Multi-satellitE Retrievals for GPM) version 6B rainfall product (Huffman et al. 2020), which merges and homogenizes data from NASA's Global Precipitation Measurement (GPM) mission with its predecessor Tropical Rainfall Measurement Mission (TRMM). All of the events considered occurred within the period during which GPM IMERG v06B rainfall data is available (2001-present). Because the satellite rainfall data spatial resolution is relatively coarse, it is not possible to effectively draw comparisons between the landslide polygons and the surrounding data in the same manner as the topographic data. However, we can still characterize the rainfall occurring during each event. We have analysed the total rainfall occurring during each of the events by accumulating the rainfall data over the period of each event indicated in Table 1, and compared this with the calculated historical 99 th percentile of daily rainfall as a way to normalize each event to the historical trends. The 99 th percentile is calculated empirically based on the GPM IMERG v06B record (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020). Since the length of rainfall period associated with each inventory varies, normalizing by the 99 th percentile for a single day provides a consistent normalizing factor for each inventory. Additionally, in Table 2 we 2 summarizes information on the landslide inventory characteristics including the 180 total landslide area, the density of landslides in the mapped area, satellite rainfall, average slope in the mapped area. Despite other studies suggesting links between event total rainfall and the density of landsliding [START_REF] Chen | Quantifying rainfall controls on catchment-scale landslide erosion in Taiwan[END_REF][START_REF] Marc | Initial insights from a global database of rainfallinduced landslide inventories: the weak influence of slope and strong influence of total storm rainfall[END_REF],

we do not observe clear links between the measured rainfall data and the macro-scale statistics of each landslide inventory.

We suggest that exploring the links between rainfall intensity as characterized by satellite measurements and the density of landsliding that results is an important topic for future research. 185

Topographic Analysis

We have analyzed the characteristics of landslide locations for the event inventories with global satellite datasets to ensure consistency across each site. These datasets are also openly available, which supports replication of these methods and findings by other authors. In Table 3, we show the datasets we have used. [Beven & Kirkby 1979, Sorensen et al. 2006] Topographic Ruggedness Index, TRI [START_REF] Riley | A Terrain Ruggedness Index that Quantifies Topographic Heterogeneity[END_REF] Topographic Position Index, TPI300 -300m wavelength [START_REF] Weiss | Topographic Position and Landforms Analysis[END_REF] Topographic Position Index, TPI2000 -2000m wavelength [START_REF] Weiss | Topographic Position and Landforms Analysis[END_REF] Forest Cover (1 arcsecond resolution)

Global Forest Change 2000-2018 [START_REF] Hansen | High-Resolution Global Maps of 21st-Century Forest Cover Change[END_REF] Forest loss since 2000 Forest cover

The DEM and forest loss data are both provided at approximately 1 arc-second resolution, which allows for direct comparison at this scale. While this resolution is not as fine as some of the imagery used to map the landslides, which can be 3m or finer, it represents the finest resolution at which these two datasets can be analysed using non-commercial, open datasets at a global extent. We utilize forest loss data derived from Landsat imagery spanning the years 2000-2018. Cells where forest loss is observed on any year from 2000 until the year in which the landslide event occurred are considered as a binary 'True' value for forest loss. This does not consider regrowth of vegetation in places where forest loss was observed many years prior to the event, and as such it is a relatively blunt tool to assess the importance of vegetation to landslide location. Not all of the topographic parameters are universally used in landslide analysis. Slope is almost universally considered for https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License. landslide modelling, but the use of others (in particular Topographic Position Index) is less common [START_REF] Reichenbach | A review of statistically-based landslide susceptibility models[END_REF].

Topographic Position Index [START_REF] Weiss | Topographic Position and Landforms Analysis[END_REF]] is a quantification of the relative position of a cell within the landscape. Negative values indicate the cell is in a topographic hollow and positive values suggest that it is elevated above its surroundings. The distance over which the neighbourhood comparison is made (TPI wavelength) determines the scale of the features resolved;

negative values at long wavelengths indicate a position in a wider valley, while at short wavelengths this would indicate steep narrow gorges. Relief indicates the difference between minimum and maximum elevation in a given window. It is a proxy for both slope as well as the size of hillslopes; higher relief zones have been shown to be associated with landslides in many locations [START_REF] Reichenbach | A review of statistically-based landslide susceptibility models[END_REF]]. Compound Topographic Index (CTI) is a measure of both slope and the upstream contributing area. In some locations CTI is correlated with soil parameters such as thickness [START_REF] Liang | Spatial and temporal variations in the effects of soil depth and topographic wetness index of bedrock topography on subsurface saturation generation in a steep natural forested headwater catchment[END_REF].

Finally, we also analyse the average upstream anglethis is the average angle from the pixel location to every cell that drains into that pixel. It provides a measure of how steep the areas are that feed into each pixel. There is a significant degree of overlap between how some of these parameters are calculated, and we recognize the importance of considering co-linearity.

In order to assess the co-linearity of the variables, we have compared each pair of variables. Pair-plots are shown in the supplementary material (Supplementary figures S1 and S2). Unsurprisingly, strong correlations are observed between slope and average upstream angle, as well as between Topographic Ruggedness and relief. It is also important to note the negative relationship observed between TPI and CTI, confirming that the hollows in the landscape are also locations where saturation state is likely to be higher. Considering these co-linear relationships, it is important to ask which variables are the most effective predictors of landslide locations for the analysed inventories. To analyse the importance of the input variables, we first perform analysis of the influence of each individual variable and then use a Generalized Linear Model to explore the effect of colinearity.

For the assessment of each parameter by itself, we calculate the relative ratios of the distributions for each variable for the topography and the landslide populations. This follows the example of other recent studies [START_REF] Marc | Initial insights from a global database of rainfallinduced landslide inventories: the weak influence of slope and strong influence of total storm rainfall[END_REF][START_REF] Milledge | Simple rules to minimise exposure to coseismic landslide hazard[END_REF]]. For both the landslide parameter distribution and the parameter distribution for the topography, we divide the values into bins, normalizing by the total size of the distribution. This essentially represents a value-frequency distribution. For each of the bins, we then divide the landslide probability by that of the topography, to obtain a ratio. Using slope as an example, this provides an estimate of the likelihood of a landslide occurrence at a given slope value compared to the occurrence of that slope in the landscape. This step is meant to explore the significance of each variable in bivariate structure.

Because landslides are triggered as a result of a complex interaction between various factors, we also analyze the inventories using a multivariate regression scheme to consider the interactions between the topographic factors. We do so by fitting a Bayesian Generalized Linear Model (GLM) assuming that the distribution of landslide presence/absence at the pixel level behaves according to a Bernoulli probability distribution, this being repeated for each landslide inventory. From each model we built, we store the information related to the regression coefficients. Because we implement a Bayesian version of a GLM, any Bayesian model provides estimates on the full distribution of each model component (e.g., [START_REF] Lombardo | Presenting logistic regression-based landslide susceptibility results[END_REF].

Before fitting the regression model, we apply a mean zero and unit variance normalization to all variables (e.g., Lombardo et al., 2018), which are expressed in different ranges and scales. This normalization allows us to better examine the modelling results in terms of contribution of each variable. In this scheme, larger absolute values of the regression coefficients refer to relatively large contribution of variables.

We also apply a feature selection algorithm to identify the significant and irrelevant variables. For this purpose, we use Least Absolute Shrinkage and Selection Operation (LASSO) technique [START_REF] Tibshirani | Regression Shrinkage and Selection via the Lasso[END_REF]. This method is particularly suggested for landslide susceptibility assessment to reduce the large number of highly correlated predictors without losing parameter interpretability (e.g., [START_REF] Camilo | Environmental Modelling & Software Handling high predictor dimensionality in slope-unit-based landslide susceptibility models through LASSO-penalized Generalized Linear Model[END_REF]. GLM fitting with a LASSO implementation is carried out by using the R (Team R, 2013) "glmnet" library, which was made available by Friedman et al. (2009). We apply this method and couple it with the 10fold cross-validation to remove non-informative covariates and to assess the modeling performance based on the area Under the Receiver Operating Characteristic curve (AUC) calculated for each landslide inventory (Hosmer and Lemeshow, 2000).

We characterize the landslides in two waysfirst, by calculating the parameter value for the scar area of the landslide, and secondly by calculating the raster values for the entire landslide body. We lack consistent data on the scar area for the landslide inventories in question, so instead we calculate an approximation of the scar area based on the geometry of each individual landslide. We utilize the method of [START_REF] Marc | Initial insights from a global database of rainfallinduced landslide inventories: the weak influence of slope and strong influence of total storm rainfall[END_REF] to extract the scar areas, based on the retrieval on polygon width from perimeter and area and the empirically supported assumption that the scar is 1.5 longer than wide (Domej et al., 2017). For each scar, we calculate the average value within the polygon area of each parameter. This avoids bias towards landslides with long runouts and effectively removes the lowest portion of the polygons which may not have the same topographic signal than the source areas. Even if the scar areas are only approximate, focusing on the upper part of the landslides is warranted for an improved understanding of the topographic control on landslide susceptibility.

The second way of characterizing the landslide -assessing the overall area of the landslide -allows us to focus on areas in the landscape that are likely to be hazardous, including areas where landslide material may end up.

To calculate the parameter distribution for the whole landslide body, we first rasterize the polygons of landslide locations to the resolution of the SRTM DEM (1 arc-second). This provides a binary raster of landslide presence. We then assess the parameter values for each of the pixels where landslides are present. This does mean that the largest landslides are most strongly represented in the distribution, but this is intentional as it permits us to focus on all of the areas affected in the landscape. It is important to note this approachcounting all pixelsis not appropriate for statistical susceptibility analysis, since it could lead to highly dependent datasets. For hazard analysis purposes, we feel it is appropriate to consider all pixels, since larger landslides are consistently more damaging, and we seek to capture the entire footprint.

In Figure 3, an example of the comparison is shown for the landslides occurring in Zimbabwe as a result of Cyclone Idai. We show upstream slope as an illustrative parameter. To compare the landslide data with the topography, we split the data into bins, using the same bins for both landslide and topography. The likelihood of the landslide and topography values are then compared with one another. To allow for more consistent comparison of inventories with diverse topography, we normalize the landslide and topography data by the median value for the parameter in question prior to splitting the data into bins [START_REF] Marc | Initial insights from a global database of rainfallinduced landslide inventories: the weak influence of slope and strong influence of total storm rainfall[END_REF][START_REF] Milledge | Simple rules to minimise exposure to coseismic landslide hazard[END_REF]. For example, in the case of slope, we calculate the median slope value for each inventory and divide the each binned interval by the median slope value calculated across the mapped area.

Finally, for each bin, we calculate the confidence interval for the comparison of topography to landslides using the method of Rault et al. (2018).

We have generated these estimates for each of the variables listed in Table 3 and for each of the landslide inventories listed in Table 1. One of the variablesforest lossis a binary variableit is calculated either as forest is lost or not. As such, we can only compare the average value for landslides and for topography at large, to obtain a relative difference in average forest loss value.

We have combined the results from each individual inventory into a single figure for each of the variables to assess relative differences, as well as which variables are most strongly associated with where landslides are mapped.

Results

Bivariate analysis

The bivariate analyses show that several of the parameters are strong predictors for the location of both the head-scarp and overall area of landslides, and while there is significant variability between the different inventories there are consistent patterns that emerge across all events. In broad terms, we find that rainfall-triggered landslides occur more often in rough, steep terrain. Results from the Compound Topographic (CTI) and short-wavelength topographic position suggest that these parameters can be used to effectively distinguish between headscarps and the entire landslide area, with a high likelihood of headscarps at low CTI values and at more positive TPI values (i.e., landscape convexities). For all metrics, we find that all studied inventories have approximately equal sampling at the median landscape value. In other words, the transition from low to high landslide likelihood is relative to the local landscape median value, not to an absolute value of the considered metric.

For all of the events, there is a general increase in landslide probability at higher slope values (Figure 4). Similarly, a strong increase in landslide likelihood is observed for average upstream slope angle (Figure 5). The distributions of the different inventories are slightly tighter than for slope, indicating that this may be a more consistently applicable variable. Specifically, we note that both scars and whole landslides are at an equal sampling at the median landscape upstream angle, strongly undersampling and oversampling the gentler and steeper slopes, respectively (i.e., proportionately more landsliding at higher slope values, and less at lower slopes). Consistent trends emerge where results are within a 95 th percentile confidence interval, although there is a greater spread of data values where results are not considered statistically significant.

The Compound Topographic Index (or wetness index), when tested for landslide scars shows higher likelihood of landslides for lower CTI values (Figure 6). This trend is negligible for whole landslide areas, with the statistically significant points showing almost no variation in landslide likelihood with changing CTI. This suggests broadly that CTI is a poor predictor for the areas where landslide hazard may be increased, but a better predictor of the source locations. The relationship between https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License. headscarp likelihood and CTI is not strongly linked with flow accumulation, despite the role that flow accumulation plays in setting CTI. In Supplementary Figure S3 we show the likelihood ratios for flow accumulation values, and no clear relationship emerges between likelihood ratio and flow accumulation. This suggests that the slope component of CTI is more important when considering headscarp locations, while the flow accumulation factor (observed to be correlated with an increase in likelihood of whole landslide areas) may be offset by the slope in the areas where landslides run-out, leading to no overall correlation with CTI and whole landslide area.

Additionally, we observe that the CTI value where landslide headscarps and topography are equally sampled is approximately the median value, and the fit for each inventory is relatively consistent.

We find that Topographic Ruggedness Index is also a relatively strong predictor for landslide likelihood, with increases in TRI correlated with increases in landslide likelihood ratio for almost all events (Figure 7), and statistically significant results observed for several of the inventories. For several events, the results are in line with prior work that has shown roughness and related metrics to be correlated with landslide occurrence [START_REF] Costanzo | Factors selection in landslide susceptibility modelling on large scale following the gis matrix method: Application to the river Beiro basin (Spain)[END_REF][START_REF] Reichenbach | A review of statistically-based landslide susceptibility models[END_REF]. While the point of equal sampling of landslides and topography is approximately the median value for the inventories analysed, the slope of the relationship diverges somewhat above and below this point. This suggests that the most heterogeneous parts of the landscape may not be as strong a predictor for landslide occurrence as areas of high slope.

There are not strong systematically consistent relationships between relief at a 1km scale and the likelihood of landslide headscarps and total areas. Some increase in likelihood is observed with increasing relief, although this saturates at relief values above the median relief. This suggests suggesting that relief alone is a relatively poor predictor for the source areas of landslides, or that the resolution of relief may be too coarse. In a few cases -Burundi, Typhoon Morakot in Taiwan, and Kii Province in Japanthere is a slightly more clear increasing relationship.

We observe a link between the short wavelength Topographic Position Index (300m assessment radius) and landslide likelihood ratios for landslide headscarps in several, but not all (i.e. not Kalmaegi, Morakot and Kii), of the events (Figure 9). Specifically, landslide headscarps are significantly more likely at positive TPI values (short wavelength landscape convexities like ridges). Although this is the case for the majority of inventories, results from both inventories in Taiwan and Dominica do not exhibit this tendency. This parameter also shows the clearest distinction between the headscarp areas and the whole landslide areas. The entire landslide area is more likely to be found at negative TPI values (landscape concavities like valley bottom). While TPI at 300m wavelength does not demonstrate quite as consistent relationships as slope or CTI, it remains a strong predictor. In particular, the larger variation between headscarps and overall landslide areas suggests that shortwavelength may be a valuable way to distinguish between scarps and deposits in a preliminary assessment.

The Topographic Position Index assessed over longer wavelengths (2000 m) does not show any significant or consistent links with landslide likelihood ratios, suggesting that TPI assessed on this scale does not effectively resolve the hillslope characteristics associated with landsliding. Since Forest Loss is a binary variable, we do not plot this across multiple bins. However, we calculate the average ratio of forest loss in landslide zones to the overall topography, and we find across all events that the value is 1.98 ±1.38 (1 standard deviation). This implies that forest loss zones are correlated with higher likelihood of landsliding. We see the largest differences between landslide zones and non-landslide zones in Salgar, Colombia, Hiroshima, Japan, and the landslides triggered by Typhoon Morakot in Taiwan (forest loss is more than 3.5 times more likely in landslides in these cases). In 4 cases, forest loss was observed as less likely in landslide pixels: in Blumenau, Brazil, Lanao del Norte, Philippines, Thrissur, India, and West Pokot, Kenya. We suggest that while forest loss prior to landslide events is generally higher in landslide locations than in the rest of the landscape, this relationship is not consistent enough to necessarily be a good predictor of landslide location by itself.

Multivariate analysis

We have used the LASSO method to quantify the importance of the different predictors for both headscarps and whole landsides, while reducing the influence of co-linearity [START_REF] Camilo | Environmental Modelling & Software Handling high predictor dimensionality in slope-unit-based landslide susceptibility models through LASSO-penalized Generalized Linear Model[END_REF]] (Figure 10).

Figures 10A and 10B also show the modelling performances, which are represented by AUC values, varying from "reasonable" (0.6<AUC<0.7) to "adequate" (0.7 < AUC < 0.8) and "outstanding" (0.8<AUC<0.9) based on AUC classes defined by Hosmer and Lemeshow, (2000). The lower AUC values for some events may indicate that we lack some key explanatory variables; crucially, this may include rainfall intensity and duration, although as discussed above we lack consistent high-resolution data to assess this within the spatial domain of the considered inventories. Other relevant parameters may include land cover, lithology and geo-structural parameters, and anthropogenic influence [START_REF] Reichenbach | A review of statistically-based landslide susceptibility models[END_REF].

Our findings show that slope, on one hand, is the factor that most frequently appears as significant in GLM run for both the landslide headscarps and the whole areas, with landslides favoring steeper locations. On the other hand, average upstream angle and CTI in GLM of the headscarps and average upstream angle, CTI and Topographic Position Index (with 300m radius) in GLM run for the whole area appear as the least commonly observed significant variables. The non-significant or low impact of most of these topographic variables is likely due to the collinearity existing between these variables (e.g., slope and average upstream slope, slope and CTI, CTI and TPI -Supplementary Figures S1 andS2).

The results indicate that except for CTI, all variables have a positive weight on classifying a given grid cell as "landslide presence" instead of "landslide absence" given the choice of predictors. There are only two cases that do not follow this general trend (i.e., the two Taiwanese inventories).

The regression coefficient of TPI calculated for the landslide headscarp areas in Kalmaegi, Taiwan has a negative sign, unlike all other cases. Overall, as we explained above, different TPI values refer to different subsections of a hillslope. Specifically, positive values refer to ridges or hillslopes, whereas negative values correspond to the valley. As a result, the negative weight of TPI on classifying the landslide presence and absence condition in the GLM is difficult to interpret. This could be caused by interactions between variables. Although we run a variable selection method (i.e., LASSO), TPI could be still interacting with the others. If it shares a similar signal to at least one another variable, the sign of the regression coefficient can be influenced by the interaction. The negative regression coefficient of TRI obtained for the whole landslide areas in Taiwan, Morakot is the other case that the response of the covariate is different from the other examples. Similar to the Kalmaegi inventory case we presented above, the negative sign could be also caused by the interactions between variables. However, this could be also associated with the physical properties characterizing whole landslide areas. TRI in Taiwan, Morakot, in particular, might correspond to smooth topography. In either case, TRI does not appear as a significant variable other than the Taiwan, Morakot.

The two inventories where negative CTI values are most significantly associated with landslide incidence -Morakot and Hiroshimahave few commonalities; their lithologies differ, and the mean slope of the affected area in Hiroshima is markedly lower than Morakot. Perhaps the most significant commonality is that the triggering rainfall exceeded the historical maxima by a significant degree (Table 3), which may increase the likelihood of failure resulting from local transient pore pressure increases, rather than due to saturated flow at the base of hillslopes. Excepting these two examples, the results show that the signal of CTI is not contributing to the GLM while classifying landslide presence or absence.

Discussion

The primary intention of this study is to assess the critical topographic parameters associated with rainfall triggered landslides, using a large dataset of landslide inventories that includes 6 newly mapped events. Our results are comparable with existing studies [e.g. [START_REF] Marc | Initial insights from a global database of rainfallinduced landslide inventories: the weak influence of slope and strong influence of total storm rainfall[END_REF][START_REF] Milledge | Simple rules to minimise exposure to coseismic landslide hazard[END_REF]] exploring landslide locations using inventories, while adding more detail and assessment of global variability, which we discuss below. First, however, we explore some of the limitations and assumptions that go into the mapping and analysis of the landslides.

Uncertainty in landslide mapping and DEM metrics extraction

Firstly, it is important to consider how representative the landslide inventories are. We have attempted to include landslide maps from a diverse set of locations around the world, but this is still only a fraction of landslides that have occurred in the last 2 decades. Some of the inventories, like the landslides occurring due to Typhoon Morakot in Taiwan, are driven by such huge rainfall events that the overall area of landsliding greatly exceeds other examples with lower rainfall. This is one of the key reasons why we have used likelihood ratios as a metric to assess landslide locations, since it does not consider the overall area of landslides triggered by a given rainfall event. Most of the inventories are drawn from locations with tropical climates [START_REF] Geiger | Klassifikation der Klimate nach W. Köppen[END_REF]], and although the pairs from Brazil and Japan sample areas of humid subtropical climates this is not a true representative sampling of climatic regimes. One exception is the landslide inventory from Zimbabwe, which is in a semi-arid climatic region. Although our examples disproportionately sample tropical and subtropical areas, these areas generally experience the highest erosion rates [START_REF] Milliman | Geomorphic Tectonic Control of Sediment Discharge to Ocean -The Importance of Small Mountainous Rivers Geomorphic / Tectonic Control of Sediment Discharge to the Ocean: The Importance of Small[END_REF], driven by increasingly intense rainfall (e.g., [START_REF] Bookhagen | Spatiotemporal trends in erosion rates across a pronounced rainfall gradient : Examples from the southern Central Andes[END_REF]. Similarly, while the inventories are drawn from places with diverse lithologies, we do not have datasets from a fully representative set of lithological locations [START_REF] Hartmann | The new global lithological map database GLiM: A representation of rock properties at the Earth surface[END_REF] While we have attempted to ensure the consistency of landslide inventories by hand-correcting the events, some inconsistencies may still exist. One important consideration is that the datasets used here do not distinguish between different landslide types, or distinguish between scar and deposit. While this is consistent across inventories, it is important when considering the results.

In particular, since we do not have constraints on whether mapped landslides are purely shallow soil slides or whether they incorporate deeper bedrock, we cannot determine differences in topographic characteristics associated with each. The change in material properties from soil to bedrock can lead to changes in overall volume mobilized for a given landslide area [Larsen et al. 2010], so inventories where smaller, shallow landslides are a larger proportion of the mapped inventory may have different characteristics. For example, the landslides mapped using aerial photography around Hiroshima, Japan, do not show particularly high likelihood ratios at very high relief or TRI values, suggesting these landslides generally occur on smaller, less rough hillslopes.

Hand mapping and correcting will help reduce the potential for landslide amalgamation [START_REF] Marc | Amalgamation in landslide maps: effects and automatic detection[END_REF], which is essential in order to estimate width and headscarps areas from landslide polygon geometry [START_REF] Marc | Initial insights from a global database of rainfallinduced landslide inventories: the weak influence of slope and strong influence of total storm rainfall[END_REF]]. Since we do not have access to the imagery for all of the previously published events, we are not able to correct these events and thus must rely on prior mapping being consistent with our own efforts. Part of the challenge of compiling different events is the different sources of imagery used to create each inventory. For most of the inventories we have mapped as part of this study, the imagery is consistent in terms of resolution, and we have benefited from the rapid return time of Planet Dove satellites to ensure that cloud cover does not mask any of the areas mapped. However, without imagery to clarify it may be possible that parts of the previously published inventories are masked by cloud cover. In addition, the inventories mapped using coarser resolution satellite imagery, such as the part of Taiwan impacted by Typhoon Kalmaegi, may not capture the smallest landslides that resulted. If smaller landslides are preferentially found in certain parts of the landscape this may introduce systematic biases in observed likelihood ratios.

While the imagery used to compile the different inventories varies in resolution, there do not seem to be consistent, systematic differences between likelihood ratios that can be explained as a result of small landslides that systematically bias the events.

For example, landslides in the Dominica events have similar likelihood ratios for each parameter compared to the landslides from Typhoon Kalmaegi in Taiwan, despite these datasets having the largest difference in effective imagery resolution.

When considering the whole landslide area, we pixelate the landslides to the resolution of the DEM to highlight the most hazardous parts of the landscape. This pixelation process can introduce a source of systematic error, since if less than half of a cell area is occupied by a landslide polygon it is still considered to be a 'landslide pixel'. Some landslides may be significantly smaller than the SRTM cell resolution if they are mapped using high resolution imagery, but they will still count as a full size pixel for the purposes of analysis as a result of the rasterization process. This introduces a potential source of bias as smaller landslides may make up a larger proportion of analysed pixels than their actual area would represent. Landslides below the approximate area of half an SRTM cell (450 square metres) make up an appreciable proportion of total landslide area in Hiroshima and Dominica (~30%) (Supplementary Figure 12). In these settings, we would expect that the influence of smaller landslides may be over-estimated at the 30m resolution of analysis, although in the majority of other inventories landslides below this cutoff represent less than 5-10% of the total landslide area (and therefore the analytical dataset of landslide pixels).

To address the potential for bias due to over-sampling of small landslides with a coarse resolution DEM, we have resampled the DEM for the events in Hiroshima and Dominica to a resolution of 10m, at which nearly all landslides are captured without size exaggeration. We then recalculate the likelihood ratios for the landslides and compare the resampled DEM results with those from the original DEM [Supplementary Figure S5]. For slope, average upstream angle, CTI, relief and TRI, only minor differences are observed between the results for a resampled DEM and the original DEM. There are some differences between TPI at 300m resolution, but no consistent relationship seems to emerge. Thus we do not think our results are affected by the coarse rasterization process, although it is likely that accessing higher resolution DEM may alter the result depending on local variable, like slope, CTI or TRI.

Other parameters are often incorporated into landslide susceptibility such as geological factors like soil characteristics or lithology, local land cover type or climatic metrics. Characterizing these parameters consistently across different inventories requires a global dataset, but the resolution of globally available, open data for rainfall, soil type, or geological parameters is too low to differentiate between landslide zones and non-landslide zones. As such, we have chosen to focus exclusively on topographic factors within our assessment.

Differences between headscarp and overall landslide area

While for several parameters, headscarps and the entire landslide area are similarly sampled at a range of values, for TPI and CTI we see significant differences across a large number of the inventories (Figure 11). Headscarps are more likely at lower CTI values, and at more positive TPI values. Positive TPI implies headscarps are more likely at concave locations in the landscape, while a lower CTI value indicates areas with lower flow accumulation and saturation. This describes parts of the landscape that sit closer to ridges. This broadly supports the assessment above that higher TPI and CTI values may be a way to distinguish between scar and deposit areas. No systematic differences are observed with respect to TRI or average upstream angle (Supplementary Figure 4) By comparing headscarps and the overall landslide area, the observations we have made provide informative contrasts with prior work. Similar recent work exploring the characteristics of earthquake-induced landslide inventories suggests that slope angle and upslope contributing area as key determinants of hazard, defined by the entire landslide areas [START_REF] Milledge | Simple rules to minimise exposure to coseismic landslide hazard[END_REF].

Our findings are consistent for entire landslide areas, but differ for headscarp area, which is poorly determined by flow accumulation [Supplementary Figure S3]. One may be surprised by the fact that landslides triggered by intense rainfall have headscarps uncorrelated with drainage area, while both earthquake and rainfall induced landslides have whole areas strongly related to it. We propose that the whole area relationship mainly reflects runout paths and not hydrological processes, and that the initiation of rainfall induced landslides poorly relates to the surface parallel hydrological flow. This is discussed in more detail below. The observed differences between headscarp and overall landslide area can be exploited to refine our understanding of susceptibility and hazard modelling, by focusing on parameters controlling headscarp areas where landslides initiate (e.g., slope, CTI), and the entire landslide area where landslides impact (e.g., drainage area, TPI), respectively. Such a focus can help support both sets of applications for a more comprehensive landslide hazard information and emphasises the need to distinguish diverse portions of mapped landslides depending on the study objective.

Implications for triggering mechanisms and landscape evolution

One of the most consistent observations that emerges from this study is that for several parameters (Slope, Average upstream slope, TRI, CTI), the critical point where landslides and topography are equally sampled is approximately the median value for the inventory in question. This is consistent with previous observations on rainfall and earthquake induced landsliding [START_REF] Marc | Initial insights from a global database of rainfallinduced landslide inventories: the weak influence of slope and strong influence of total storm rainfall[END_REF][START_REF] Milledge | Simple rules to minimise exposure to coseismic landslide hazard[END_REF]. For average upstream slope and CTI, the relationships for different inventories are in fact very similar; this is despite a large variation in the median slope for each of the inventories (Table 2). This suggests that landslide likelihood is strongly dependent on the median topography, rather than a specific critical angle. This implies two important points: first, that despite important differences in the landscapes observed, consistent hazard relationships can be defined based upon median landscape values, and second, that these diverse landscapes may be in a form of long-term equilibrium with respect to their landslide behaviour.

We suggest that each of the considered landscapes, with its own lithology, vegetation, climate and tectonic forcing, may have evolved such that local hillslopes have slope gradients and hydromechanical properties that set the possibility for landslides on the upper half of the distribution. Evolution of the hillslopes' regolith state under climatic forcing is predicted by geomorphological models of hillslope stability coupled with stochastic rainfall forcing [START_REF] Dietrich | A process-based model for colluvial soil depth and shallow landsliding using digital elevation data[END_REF][START_REF] Iida | A stochastic hydro-geomorphological model for shallow landsliding due to rainstorm[END_REF][START_REF] Iida | Theoretical research on the relationship between return period of rainfall and shallow landslides[END_REF].

Landscape evolution towards a critical state was also inferred to explain why landsliding in the Kii peninsula better matched relative rainfall anomaly rather than absolute rainfall patterns [START_REF] Marc | Spatial Patterns of Storm-Induced Landslides and Their Relation to Rainfall Anomaly Maps[END_REF].

Alongside the implications for landscape evolution and how to derive susceptibility metrics, our results also offer insight into the mechanisms of landslide triggering in extreme rainfall events. By focusing on the headscarp areas, we observe that landslides are more likely in locations with lower CTI and higher TPI valuesparts of a landscape near ridges with a generally lower propensity for water saturation. This is somewhat in contrast to studies that suggest rainfall-triggered landslides are more likely to occur in areas lower down hillslopes where fluid saturation is greater [START_REF] Densmore | Topographic fingerprints of bedrock landslides[END_REF][START_REF] Meunier | Topographic site effects and the location of earthquake induced landslides[END_REF], possibly because they did not clearly differentiate scar from whole landslide area which are very different relative to these two metrics [Figure 11]. Anyway, the relationship with CTI and drainage area also suggests that modeling landslides under the assumption of regolith saturation due to slope-parallel, steady state flow (e.g., Montgomery and Dietrich 1995) may be inadequate. Instead, the pore-pressure triggering landslides in extreme rainfall events may rather be controlled by transient, vertical infiltration, and/or preferential flow paths [Iverson, 2000[START_REF] Montgomery | Instrumental record of debris flow initiation during natural rainfall: Implications for modeling slope stability[END_REF][START_REF] Hencher | Preferential flow paths through soil and rock and their association with landslides[END_REF][START_REF] Bogaard | Landslide hydrology: from hydrology to pore pressure[END_REF]. This recalls the essential challenge for developing modeling approaches that can account for such complex hillslope hydrology as well as with highly variable hydromechanical properties of the regolith. Nevertheless, we also suggest that future studies should compare the results from this analysis of landslides triggered by extreme rainfall with landslide inventories resulting from longer duration, lower intensity rainfall events, to assess whether the relationship with CTI and TPI changes. Indeed, we might expect that lower intensity rainfall would trigger landslides at parts of the landscape with higher CTI values as steady state saturation may be more widespread.

Finally, for some events, including Typhoon Morakot in Taiwan and Cyclone Idai in Zimbabwe, there is a small decline in relative landslide probability at very high slope values (> 35-40 degrees) [Figure 4]. It is possible that these slopes, which are generally above the angles considered to be critically unstable [Selby 1982[START_REF] Roering | Hillslope evolution by nonlinear creep and landsliding: An experimental study[END_REF]] may represent areas where landslide likelihood is reduced as a result of non-topographic factors, such as local lithological bedding plane angles [START_REF] Guzzetti | The Influence of Structural Setting and Lithology on Landslide Type and Pattern[END_REF], Santangelo et al. 2015], or thinner soils limiting the availability of material that can be mobilized as landslides [START_REF] Prancevic | Decreasing landslide erosion on steeper slopes in soil-mantled landscapes[END_REF]]. The decline in landslide likelihood at the highest slope values may represent the limit to which local pore pressure as a result of extreme rainfall can influence triggering.

Conclusions

In this study we have combined 10 existing rainfall-induced landslide inventories from a range of mountainous regions with 6 new inventories mapped as part of this study. We suggest that providing newly mapped inventories is a valuable service for the landslide community at large, and we anticipate that these inventories can provide data to calibrate and validate susceptibility and hazard models both in the specific locations where landslides occurred but also further afield. In addition, we have used moderate resolution open source satellite data to assess the parameters that characterize the location of landslides in these inventories. We find that alongside the previously documented importance of slope and topographic ruggedness, average upstream angle and topographic position are also determinants of landslide likelihood in a given location. After normalizing the topographic variables by the local landscape median, we find consistent relationships across the different inventories despite the variety of lithological and topographic settings. This suggests that relative metrics should be considered to perform landslide susceptibility analysis and that different landscapes can be at a state of equilibrium with respect to the likelihood of landsliding. The importance of multiple topographic factors to determine the local landslide likelihoods highlights the value of high resolution DEM data. While we have used the 1 arc-second resolution SRTM data, higher resolution DEM data are increasingly available. Given that we are able to map landslides at finer and finer resolution as very-high resolution satellite imagery becomes available, combining these new detailed inventories with DEMs of similar resolution is likely to provide further insights about landslide location within the landscape.

While we have not undertaken a detailed assessment of the rainfall that triggered these landslides, we emphasise that variability in rainfall is likely to explain a significant degree of variability in where landslides occur [e.g., [START_REF] Marc | Spatial Patterns of Storm-Induced Landslides and Their Relation to Rainfall Anomaly Maps[END_REF]. Future work should assess each of these inventories with respect to the rainfall that triggered the significant landsliding could yield important insights into the relationship between intense rainfall and landslide occurrence. slides for the event, Ntot (see [START_REF] Malamud | Landslide inventories and their statistical properties[END_REF]. In the lower figure (C), the size of the points depends on whether the difference between landslide and topography exceeds the calculated confidence interval for that bin interval; larger points indicate significant deviation (p>0.95), and small points indicate the difference is not significant at that probability level.

  https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

  and has been used to map landslides occurring in the https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

  https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

  show the maximum 3-hour rainfall intensity for each of the events, normalized by the historical 99 th percentile of daily rainfall. The normalized total event rainfall and normalized 3-hour rainfall provide a side-by-side comparison of the overall rainfall accumulation and the maximum intensity. The values for both total event rainfall and maximum 3-hour rainfall are calculated as the average across all IMERG https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License. grid cells in the area of the inventory. Table

  https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

  https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

  https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

  https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

  https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

  https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

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  R.E., P.A. and D.K. are supported by a NASA DISASTERS program grant 18-DISASTER18-0022. All authors were involved in study conceptualisation and writing of the manuscript. R.E., P.A. & O.M. conducted landslide mapping. R.E., H.T. & O.M. conducted data analysis.

Figure 1 :

 1 Figure 1: Locations of landslide inventories considered in this study. Locations labelled in red have been published previously,while those in blue are presented for the first time here. Satellite images of the newly mapped landslide inventories can be 755 found in the Supplemental material. Table1contains the details of each of the inventories, organised in alphabetical order.

Figure 2 :

 2 Figure 2: Probability density for landslides in each event inventory, obtained as the number of landslides with areas falling into logarithmic bins (consistent bins for all inventories), N[A:A+dA], normalized by the bin width, dA, and the total number of 760

  https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

Figure 3 :

 3 Figure 3: Example of landslidetopography ratio comparison for landslides in Zimbabwe triggered by Cyclone Idai. This shows the distribution of values for landslides (A) and topography (B) for slope. The lower part of the figure (C) shows the relative ratio of the two distributions for the parameter. The black lines in parts A and B illustrate the mean value of the data.

Figure 4 :

 4 Figure 4: Landslide likelihood ratio against the slope normalized by the median of the local landscape, for the scar area (left)and the whole landslide area (right). The size of the points depends on whether the difference between landslide and topography exceeds the calculated confidence interval for that bin interval; larger points indicate significant deviation (p>0.95), and small points indicate the difference is not significant at that probability level.

Figure 9 :

 9 Figure 9: Same as Figure 4 but for Topographic Position Index (however, here we omit normalization given that TPI is a zero centered variable) with an analysis window radius of 300m. 795

Figure 10 :

 10 Figure 10: Figure showing regression coefficients and corresponding AUC values calculated from fitted GLM for each landslide inventory, considering scar (a) or whole landslide area (b). The error bar around corresponds to the 95% confidence intervals of the AUC distribution across 10-fold cross-validation replicates. Regression coefficient are not shown for predictors

Figure 11 :

 11 Figure 11: Likelihood ratio of landslide headscarp areas compared with entire landslide area. Specifically, this shows the probability of a scar at a given CTI value, normalized by the probability of that CTI value, divided by the probability of the entire landslide at a given CTI value, normalized by the probability of that CTI value. Higher values indicate that headscarps are more likely than whole landslide areas, at that parameter value. Left figure shows the result for CTI; right figure for short wavelength TPI.

Table 1 :

 1 Details of landslide inventories analysed in this study. 140

	Location	Event	Date		Reference		Imagery (resolution)	Dominant GLiM
		triggering							lithology
	Micronesia (A)	Cyclone	2 nd	July	Harp et al. 2004		Aerial	Photographs	Basaltic / andesitic /
			2002				(varies)		trachytic lava flows
	South Taiwan (B)	Typhoon	15-18 July	Chen et al. 2013,	Landsat 5 (30m)	Sedimentary	/
		Kalmaegi	2008		Marc et al. 2018			metamorphic
	Blumenau, Brazil (C)	Prolonged	20-25 Nov	Marc et al. 2018	Google Earth / Landsat 5
		intense rain	2008				(3-30m / 30m)	Metamorphic
	Taiwan (D)	Typhoon	6-9	Aug	Chen et al. 2013,	FORMOSAT-2 / Landsat
		Morakot	2008		Chang et al. 2014,	5 (4m / 30m)	Sedimentary	/
					Marc et al. 2018			metamorphic
	Teresopolis, Brazil (E)	Local Storm	11-13 Jan	Marc et al. 2018	Google Earth / Landsat 5 /
			2011				EO-ALI (3-30m / 30m /	Acid Plutonic /
							30m)		metamorphic
	Kii Province, Japan (F)	Typhoon	2-5	Sept	Marc et al. 2018	Aerial	photographs/	Sedimentary / minor
		Talas	2011				Google Earth / Landsat 5	plutonic	/
							(Varies / 3-30m / 30m)	metamorphic
	Salgar, Colombia (G)	Local Storm	17-18 May	Marc et al. 2018	Sentinel 2 / Google Earth
			2015				(10m / 3-30m)	Metamorphic
	Hiroshima, Japan (H)	Prolonged	28 Jun -9	Association	of	Drone / Aerial imagery
		intense rain	July 2018	Japanese		(varies)		Plutonic Acidic /
					Geographers,				Volcanic Acidic /
					2019				minor siliciclastic
	Zimbabwe (I)	Cyclone Idai	15-19 Mar	This study		Planet Dove (3m)	Metamorphic	/
			2019						minor siliciclastic
	Itogon, Philippines (J)	Cyclone	15-20 Sept	This study		Planet Dove (3m)	Mixed sedimentary /
		Mangkhut	2018						minor	acidic
									volcanic
	Lanao del Norte, Philippines	Tropical	20-26 Dec	This study		Planet Dove (3m)
	(K)	Storm	2018
		Tembin							Volcanic acidic
	Dominica (L)	Tropical	25-28 Aug	van Westen 2016	WorldView 3 (1.8m)	Intermediate
		Storm Erika	2015						Volcanic
	Dominica (M)	Hurricane	18-22 Sept	van Westen &	Pleiades (0.5m)	Intermediate
		Maria	2017		Zhang 2018				Volcanic
	Burundi (N)	Prolonged	3-5	Dec	This study		Sentinel 2 (10m)
		intense rain	2019						Metamorphic
	Thrissur, India (O)	Prolonged	7-18 Aug	This study		Planet Dove (3m)	Metamorphic	/
		intense rain	2018						Plutonic acidic
	West Pokot, Kenya (P)	Prolonged	22-25 Nov	This study		Sentinel 2 (10m)
		intense rain	2019						Metamorphic

Table 2 :

 2 Macro-level characteristics for events discussed, including rainfall statistics. Note that median slope values have been calculated by excluding very low slope values (<1 degree) to remove lakes and oceans.

	Event Name	Number of	Total Area	Density of	Median	Total	Std.		Total	Std.	Maximum	Std. dev
		landslides	(km 2 )	landslides	slope	Event	Deviation	Event	deviation in	3hr rain /	3hr rain /
				(m 2 /m 2 )	(degrees)	rainfall	in	Event	rainfall /	event	Historical	Historical
						(mm)	rainfall	Historical	rainfall/	24hr 99 th	daily 99 th
									99 th	historical	percentile	percentile
									percentile	99 th pctl.
	Micronesia (A)	273	1.949	3.62E-02	12.0	1426.2	85.6	24.7	1.5	11.2	0.4
	South Taiwan (B)	429	3.650	3.33E-04	25.5	517.1	103.7	6.6	1.7	2.5	1.1
	Blumenau, Brazil (C)	597	5.847	2.11E-03	15.3	72.8	37.0	1.5	0.7	0.3	0.35
	Taiwan (D)	10236	205.048	7.43E-03	23.7	1114.0	183.7	14.6	4.0	2.1	1.42
	Teresopolis, Brazil (E)	7268	21.560	7.76E-03	20.8	193.2	54.3	5.4	1.6	1.6	1.0
	Kii Province, Japan (F)	1901	12.258	1.51E-03	25.4	284.5	46.2	4.3	0.5	1.3	0.6
	Salgar,
	Colombia	131	0.283	4.75E-03	27.44	112.2	34.0	3.5	1.3	1.4	1.8
	(G)
	Hiroshima, Japan (H)	9275	4.542	1.06E-03	14.1	488.2	62.0	10.6	1.1	4.1	0.9
	Zimbabwe (I)	1319	2.554	1.62E-03	13.3	321.0	30.0	8.7	0.7	3.6	0.9
	Itogon,
	Philippines	458	0.627	1.04E-03	26.1	179.3	12.5	4.0	0.5	1.5	0.7
	(J)
	Lanao del
	Norte,	17	0.195	8.36E-04	16.3	150.6	22.7	5.6	0.9	2.2	1.5
	Philippines

https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

Table 3 :

 3 Analysis datasets. Explanation of each of the variables in found in the accompanying text.

	Dataset	Source / Reference	Parameters from Dataset
	SRTM	SRTM Non-Void Filled	Relief (1km radius)
	DEM (1-arc	https://doi.org/	Slope
	second	10.5066/F7K072R7	Average upstream angle
	resolution)		Compound Topographic Index, CTI

Table 1 ]

 1 .

Acknowledgements

https://doi.org/10.5194/nhess-2021-250 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License.

Data Availability

All data used in this study is provided in the supplementary material, and all methods are detailed above.

Declaration of Competing Interests

The authors declare that they have no conflict of interest.


G A Farzi

E Bourgeat-Lami

T F L Mckenna
email: tim.mckenna@chee.queensu.ca

Miniemulsions Using Static Mixers: Part 2. Co-emulsification and composite materials using SMX static mixers

Keywords: Emulsification, Static mixer, Droplet size, Miniemulsion polymerisation, Hydrophobicity, Silica Particles, Nanocomposite

A 50:50 mixture of methylmethacrylate (MMA) and butyl acrylate (BA) was emulsified, then polymerised using different static mixers. It was shown that the emulsification behaviour was very different from that observed for MMA alone under similar conditions. It was shown that the hydrophobicity of the monomers had a strong influence on the droplet size and stability.

It was also shown that the amount of work done on the emulsion is important for obtaining polymerisable droplets, and that monomer systems that are difficult to miniemulsify with a low energy system can in fact be made to form stable emulsions simply by changing the emulsification conditions. Finally it was shown that when the miniemulsification conditions are correctly chosen, it is possible to generate miniemulsion dispersions containing silica that can be successfully polymerised to produce silica/polyacrylic nanocomposites.

Introduction

A polymerisation system for the production of polymeric latex generally consists of five principle components including, continuous phase (generally water), surfactant(s), monomer(s), a hydrophobic agent and initiator. 1 In this paper we will focus on miniemulsion systems rather than macroemulsions (conventional emulsion polymerisation). Miniemulsion polymerisation preserves certain advantages of conventional emulsion polymerisation in that it allows us to use the same (or similar) monomer and reactor systems, while overcoming some of its limitations and opening the door to novel applications. [1][2][3] The main difference between conventional and miniemulsion polymerisation lies in the mechanism of particle creation. [1][2][3] In conventional emulsion polymerisation micellar nucleation is typically the principle means of particle formation. In miniemulsions, the droplets are formed by imposing shear stress on a mixture of all of the reactants before the reaction begins. If this is done correctly, the droplets will be small enough to successfully capture free radicals generated in the aqueous phase (using the same type of initiator system as in macroemulsions), and will behave as small individual reactors; ideally becoming particles in a 1 to 1 copy. This means that oil soluble compounds or hydrophobised inorganic materials can be directly integrated into the polymer particle ab initio to make hybrid or composite materials, respectively. Of course, this can be done in conventional macroemulsion systems, but it is significantly more difficult. In addition, the creation of particles prior to the reaction can be of benefit as this allows one to control the initial state of the polymerisation in a manner that cannot be done in emulsion systems.

The first essential step in miniemulsion polymerisation is therefore the emulsification of the oil and water phases using some type of high shear mixer in order to break up the monomer phase in to nanodroplets, and reach average droplet diameters on the order of 50-300 nm. A variety of devices including ultrasonic dismembrators (US), high-pressure homogenisers, 4,5 rotor stator mixers (RS), 6,7 ultra-turrax homogenisers and stirring have been used for the formation of droplets in miniemulsion range; i.e. with diameters on the order of 100-500 nm. 8,9 US is convenient for laboratory investigation because it is rapid, can be used for viscous fluids and can make very small droplets. On the other hand, it is not particularly well-adapted for industrial production, whereas devices like rotor stator and high pressure homogenisers can be used to create a homogenous miniemulsion with small particles on a commercial scale. 9 Homogenisation devices for miniemulsification have been discussed in a number of recent papers, and reader is referred to them for more information. 2,3,10,11 In this paper, we will focus on the use of static mixers, for the reasons discussed in Part 1 of this work. 12 Very briefly, static mixers (SM) are very commonly used in industrial situations, are commercially available, and can be used in continuous processes. We have shown that they are viable emulsification devices; however it is necessary to further our understanding of the miniemulsification process with this type of device.

Static mixers (also referred to as motionless mixers) are solid elements of appropriate shape with no moving parts that are placed in a tube, and liquid (or mixture of phases) is circulated over them using a pump. They work by successively dividing, rotating and recombining the flow, and provide very uniform mixing with lower shear rates than one finds in US or RS type mixers and relatively low energy requirements. 6,12,[START_REF] Bakker | Laminar flow in static mixer with helical elements[END_REF][START_REF] Bone | Etude d'un procedes de fabrication de microcapsules par emulsification dans un melangeur statique[END_REF] Very few reports can be found in the literature related to the use of static mixers as devices for miniemulsification. To the best of our knowledge, Ouzineb et al. 6 were the first to propose SM as a means of generating miniemulsions, and compared them to RS and US as means of generating miniemulsions of styrene or butyl methacrylate. They showed that SM used significantly less energy per kilo of latex than the other devices.

In Part 1, we have shown that it is possible to control the average droplet size of MMA miniemulsions by varying the flow rates through the mixing elements, the number of elements in series, and the surfactant concentration. 12 However it turns out that while a given set of emulsification conditions (device, flow rates, emulsification times) works for one formulation, small changes in composition might make it difficult or impossible to generate a polymerisable dispersion of droplets using the same conditions. In the current paper, we present an investigation of the differences between emulsifying a single monomer and emulsifying mixtures of monomers of different water solubilities. In addition, the role of the configuration of the static mixers that make up the emulsification system on droplet size, stability and ease of polymerisation (in the sense that we obtain a 1:1 mapping of droplets into particles) were examined. Once appropriate conditions were identified, they were used to investigate the possibility of producing silica-polyacrylic composite materials.

Experimental

Materials

The monomers used in this study were methylmethacrylate (MMA), butyl acrylate (BuA), and styrene (STY) all obtained from ACROS. The hydrophobic agents, n-hexadecane (HD, 99%) and octadecyl acrylate (ODA, 97%) were obtained from ACROS and ALDRICH, respectively. All compounds were used as received. Disponil A3065 and Disponil FES 32S are non-ionic and anionic surfactants, respectively. They were graciously supplied by COGNIS France as a solution of 65 and 32 percent active matter in water, respectively. Sodium dodecyl sulphate (SDS) was obtained from ACROS and used as received. Deionised water was used as the continuous phase.

The aqueous silica suspension used in this study was graciously supplied by Clariant (France). The main characteristics of this suspension, referred to as GEN33 are the following: the specific surface area was determined from nitrogen adsorption isotherms to be 50.5 m 2 /g, the diameter of the silica particles and polydispersity index (PI) were determined by DLS using a Malvern Autosizer and were 78 nm and 0.02, respectively. The solid content and the suspension pH were respectively 27% and 9.57. -methacryloxy propyl trimethoxysilane (MPTMS, Acros organics) was used as coupling agent through this work. [START_REF] Bourgeat-Lami | [END_REF] Absolute ethyl alcohol (99.8%) and methyl alcohol (99.9%) were obtained from Carlo Erba, and used as received.

Miniemulsification procedure

Miniemulsions were prepared using 2 formulations. When SDS was used as the surfactant, 0.14 g SDS was dissolved in 70 g water in one beaker that was mixed for 30 minutes using a magnetic stirrer bar at room temperature. The hydrophobic agent (1.4 grams of HD) and 28 grams of monomer (MMA or a 50:50 w/w mixture of MMA and BA) were mixed in another beaker. In the case where the mixed surfactant system was used, the aqueous phase was prepared by dissolving 0.17 g of the anionic surfactant and 0.26 g of the non-ionic surfactant (these amounts refer to the active fraction of the surfactants) in 70 g of deionised water. The oil phase was prepared by mixing an appropriate amount of hydrophobic agent (ODA or HD, amounts specified below) in the monomer(s). Each of the oil and aqueous phase mixtures for a given formulation were stirred separately using a magnetic stirrer for approximately half an hour. The organic phase was then added to the aqueous phase under gentle agitation with a magnetic stirrer and then emulsified.

Figure 1 shows a general configuration of SM assembly in which the mixture of the two phases is placed in a reservoir with a magnetic stirrer, and then circulated through a tube (or tubes) containing the SM elements. The two types of SM investigated here are shown in Figure 2. In the initial part of this study, polyacetal mixers (PAC) were used for emulsification (see Part 1 for more details). 12 In this case, the SMs were housed in a tube with an interior diameter (ID) of 1 cm and a length of 100 cm, each containing bundles of 4 mixing elements 5 cm in length and 6.4 mm in diameter. When SMX elements were used, they were housed in a polytetrafluoroethylene (PTFE) tube with an interior diameter of 8mm.

The elements themselves were 8 mm in length and 8 mm in diameter, and 7 of them were housed in the PTFE tube. Ultrasonication (US) was used as reference homogenisation device. Sonication was performed using a Branson Ultrasonic dismembrator (model CV26) set at 480W.

Miniemulsion polymerisations

The miniemulsion polymerisations were carried out in a cylindrical glass batch reactor (150 mL) with a nitrogen inlet for all the samples. After introduction of the miniemulsion into the reactor, nitrogen was bubbled through the solution for 30 minutes in order to eliminate the oxygen before beginning the polymerisation process. Once this step was completed, the mixture was brought to the desired reaction temperature and the initiator, APS, was added to the batch reactor.

The reactor contents were mixed during polymerisation with a glass anchor stirrer at a constant speed of 250 rpm and the temperature was kept constant at 70°C, using water circulation from a thermostatic bath. Samples were periodically withdrawn to follow the particle size and size distribution, as well as conversion which were measured by gravimetry.

Characterization

The intensity average droplet and polymer particle size and polydispersity of miniemulsions or latexes were measured with a Malvern Autosizer. The miniemulsions were considered stable if there was no change (within estimated experimental error of 10 nm) in the average droplet size after approximately 4 hours. Complete droplet size distributions reported for the miniemulsions were measured using the Beckman-Coulter LS-230 (Static Light scattering).

The ratio of the number of particles to the number of droplets (N p /N d ) was monitored during the reaction and plotted against conversion.

Results and Discussion

Miniemulsion of MMA/BuA mixtures

The main objective of this work is to study the effect of a mixed monomer system (MMA/BuA 50/50 wt%) and to find the acceptable conditions for miniemulsification of this mixture and its subsequent polymerisation. An example of the challenge posed by this problem is illustrated in Figure 3. It was shown in Part 1 that it was possible to create a MMA miniemulsion with a volume average diameter of 212 nm after 30 minutes of homogenisation over the PAC mixers at a flow rate of 61 mL.s -1 using the SDS formulation described above.

However, when the same formulation and homogenisation conditions were applied to a 50:50 (w/w) mixture of MMA and BA, a bimodal droplet size distribution is obtained. The smaller, well-defined mode had a much larger volume average droplet size of 320 nm. Polymerisation of these samples resulted in a latex with particles considerably smaller than the miniemulsion droplets leading to a N p /N d ratio of 5.2 (using the 320 nm diameter mode for the calculation). This means that significant particle renucleation occurred in this system. On the other hand, emulsification of the MMA+BA samples using US for 120 seconds led to a stable miniemulsion with a volume average droplet size of 155 nm (vs. 130 for MMA alone in Part 1 under the same conditions), and a relatively narrow droplet size distribution. Polymerisation of this sample showed that N p /N d = 0.95 throughout the reaction, suggesting that droplet nucleation was predominant. Clearly even moderate changes in formulation can have a large impact on our ability to create a stable dispersion. The PAC set-up cannot be used to make a stable miniemulsion of MMA+BA, and while US is a feasible alternative in this case, the average droplet diameter is almost 20 percent larger for the mixture than for MMA alone (a 72% increase in the average volume). However it remains to be explained why one can make a dispersion of MMA+BA with the US set-up, but not with the PAC static mixers. In order to better understand the relationship between the formulation and the emulsification step, additional homogenisations were performed using single monomer systems with the formulations shown in Table 1. This mixed surfactant system was chosen in an attempt to improve upon the results in Figure 3. The droplet size distribution of three different monomers of different water solubilities are shown in Figure 4, the evolution of the volume average droplet size of these miniemulsions as a function of homogenisation time is shown in Figure 5, and the droplet size distributions of MMA+BA emulsions made using the mixed surfactant formulation and the two different homogenisation systems discussed until now are shown in Figure 6.

First of all, it can be seen that once again, the PAC set-up can be used to generate a stable MMA miniemulsion with an average particle size of 200 nm. While this is slightly smaller than those obtained with the SDS-based formulation (212 nm in Part 1), the difference between the two is within the limit of sensitivity of the apparatus used for this measurement so it is fair to say that the mixed surfactant system gives essentially the same results as the SDS system, leading us to believe that the results of the two formulations are comparable.

Interestingly enough, the results in Figure 4 shows that it is possible to use the SM setup with the PAC mixers to emulsify BA alone. Thus this set-up can be used to make MMA miniemulsions, BA miniemulsions, but, as shown in Figure 6, not for the mixture of MMA+BA even with this new formulation. In addition, it appears that it is not possible to obtain a monomodal miniemulsion of styrene. Once again, using the same formulation, one can make a stable, monomodal miniemulsion of the MMA+BA mixture using the US as the homogeniser. , respectively. [START_REF] Brandrup | Polymer hand book[END_REF] Formulations are given in Table 1.

Figure 5. Evolution of the volume average droplet diameter for three different miniemulsifications using the PAC mixture and the formations in Table 1 for MMA, BA and STY as monomers. Figure 6. Droplet size distribution in miniemulsions of MMA+BA created by PAC static mixers and US for the formulations given in Table 1.

In order to understand the relationship between the impact of a change of formulation on the droplets generated in this manner, let us consider equation (1), that, in an ideal case (i.e. no coagulation or heat loss during emulsification), relates the energy required to break up droplets in a 2 phase system to form a surface area A (we will assume that the initial unemulsified system has a surface area of approximately zero):

W breakage = A =N p  Vd 2 Equation 1
where  is the oil droplet/water interfacial tension, A is the newly developed surface of droplets generated by homogenisation, N p is the number of particles per unit volume of emulsion, V the emulsion volume, d the average particle diameter, and W breakage is the work needed to generate this surface area. This expression can be rewritten in terms of d: Equation 2This expression tells us that the droplet diameter will vary as the inverse of the square root of the interfacial tension. Of course, this is an approximate representation of reality since it does not take into account the droplet size distribution, coalescence, heat losses, imperfectment mixing, etc. However it demonstrates clearly the relationship between the energy used for homogenisation and the formulation of the miniemulsion.

The interfacial tension of the four monomer systems investigated here (for the formulations in Table 1) was measured using the droplet volume method [START_REF] Lando | [END_REF] , and the values for MMA+BA miniemulsions, MMA, BuA and STY are shown in Table 2. It can be seen from this table that the interfacial tension of the mixed monomer system is higher than that of MMA (and of BA also), but very close to that of STY. Therefore, if one wishes to obtain the same droplet size for both above emulsion systems, it would be necessary to do almost twice as much work on the MMA/BA system and the STY, than for MMA alone. The outcome of this analysis is that in order to emulsify the two monomer system (MMA/BA mixture or STY), it will be necessary to change the physical characteristics of the homogenisation set-up and/or the formulation. That a change of formulation only mildly improved the creation of a mixed miniemulsion, suggests that it is necessary to look at the impact of the mixing equipment on the droplet formation process. In addition, the fact that one can create stable miniemulsions using the US also suggests that the difficulties encountered in emulsifying the MMA/BA system are due more to the equipment than to the formulation. Since we wish to concentrate on using homogenisation systems that can be scaled up to pilot and commercial levels, US is not an option, so it was decided to look at the impact of the flow rate and the type of static mixer.

Two modifications were made to the emulsification set-up, while keeping the same general configuration as shown in Figure 1. First, the PAC mixers were switched out in favour of the SMX mixers in a much shorter tube. A comparison between the two types of static mixers based on droplet evolution using the SDS formulation for MMA alone was performed. The results of the evolution of the droplet size distribution are shown in Figure 7.

It is clear that all things being equal, the SMX mixers allow us to obtain smaller droplets. The SMX mixers were therefore retained for the rest of the experiments presented in this study. The second modification to the set-up was to increase the energy dissipation in the SM zone, by replacing the original pump with one that allowed us to increase the flow rate from 61 mL.s -1 to 133 mL.s -1 . The modified set-up was then used to explore the possibility of making polymerisable miniemulsions of a mixture of MMA/BA.

The droplet size distribution of a miniemulsion after 30 minutes of homogenisation of the mixture defined in Table 1 at a flow rate of 133 mL.s -1 over the SMX mixers is shown in Figure 8. This can be compared to the DSD of the same formulation with the PAC mixer shown in the previous section (Figure 3). Clearly the higher levels of energy dissipation available with this configuration allow us to break up the larger droplets that remain in the PAC system.

Figure 8. Droplet size distribution of MMA+BuA miniemulsion after 30 minutes homogenisation with sulzer SM (solid line) compared to the DSD obtained using the PAC emulsifier (dotted line) using the formulation in Table 1.

The MMA+BA droplets generated in this manner after 30 minutes of homogenisation, were polymerised as described above. After 2 hours of reaction, the overall conversion was 97%, and the value of N p /N d =1.11, demonstrating that these droplets could be successfully polymerised.

Once MMA+BA droplets were successfully polymerised in this manner, hybrid MMA/BA miniemulsions containing different amounts of silica were prepared from a master batch of a relatively high concentrated dispersion of MPTMS-functionalised silica in monomers (35wt % silica relative to MMA/BA 50/50 by weight) by diluting it to the desired concentration by adding monomer(s) prior to homogenisation. The MPTMS-functionalised silica was prepared using a procedure similar to that of Qi et al. 18 Stable miniemulsions were created by homogenisation of silica-containing monomer dispersions in aqueous solution of surfactants using the set-up in Figure 1 and the improved process described above (SMX mixer, flow rate of 133 mL.s -1 ). The evolution of droplet size as a function of homogenisation time is illustrated in Figure 9 for different silica contents. As can be seen, the droplet size decreases as a function of homogenisation time as expected. The results also show that the droplet size increases with increasing silica content. The increase was moderate for low silica contents and became more important when the silica concentration increased to 15wt%. Note that similar sizes were obtained for 15wt% and 20wt% silica. This could be due to the fact that for silica contents higher than 15%, the viscosity of the dispersed phase is relatively high and the energy dissipated by SM might not be sufficient to break up the droplets. It is worth mentioning that similar results have been reported in the literature both for silica particles 18 and titanium dioxide. [19][20][21] The evolution of the polydispersity index (PDI) of the DSD of the miniemulsions as a function of silica content is plotted in Figure 10. It can be seen that the PDI increases as the silica content is increased. Again similar results were obtained by Qi et al. for silica. 18 This suggests that the higher the silica content, the more difficult it is to maintain the stability of the droplets which leads to an increase in droplet size and droplet size distribution.

Conclusion

It was shown that the emulsification of MMA+BA mixtures using PAC static mixers did not lead to the production of stable, well-defined miniemulsions regardless of the stabilisation system used. Similar experiments using US as homogenisation device showed that it is nonetheless possible to create polymerisable miniemulsions. An analysis of the interfacial tensions showed that while enough work can be done on either an MMA dispersion or a BA dispersion to make stable miniemulsions using the PAC, this was clearly not the case with the MMA+BA mixture because of its high interfacial tension. A similar conclusion was reached for STY dispersions for the same reason.

By changing the static mixers and using a more powerful pump, it was shown possible to make MMA+BA miniemulsions using SMX mixers. The resulting miniemulsions were successfully polymerised. Finally, this set-up was used successfully to produce silicacontaining polymer particles. The majority of droplets were nucleated upon polymerization when less than 15% silica was used. However, when the silica content exceeded 15%, N p /N d increased to value much higher than 1 indicating the occurrence of homogeneous nucleation.

Figure 1 .

 1 Figure 1. Schematic diagram of the emulsification set-up for the static mixer.

Figure 2 .

 2 Figure 2. Static mixers used in this study. Top: PAC mixers and bottom: SMX mixers by Sulzer (courtesy of Sulzer Chemtech).

Figure 3 .

 3 Figure 3. Droplet size distributions in miniemulsions of MMA/BuA (50/50) and of MMA alone created by PAC static mixers and by US. The volume average droplet size is 320 nm for PAC and 155 for US. The formulations were similar: 1.4 g/l SDS, 14 g HD, 280 g monomer, 700 g deionised water. The monomer was either 100% MMA or a 50:50 (w/w) mixture of MMA and BA.

Figure 4 .

 4 Figure 4. Droplet size distribution in miniemulsions of MMA, of BA, and of Styrene created by PAC static mixers. The water solubilities of STY, BA and MMA are 3.5, 11 and 150 mmol.L -1 , respectively.[START_REF] Brandrup | Polymer hand book[END_REF] Formulations are given in Table1.

Figure 7 .

 7 Figure 7. Droplet evolution over time generated using the PAC and SMX mixers for MMA and SDS.

Figure 9 .Figure 10 .Figure 11 .Figure 12 .

 9101112 Figure 9. Evolution of droplet diameter versus homogenisation time.

Table 1

 1

			. Miniemulsion recipe
	Water	Monomer	Hydrophobic agent	Surfactant	Initiator
	69.35 g	28.1 g	2g (ODA)	0.17g TA, 0.26g TN	0.12g APS
	TN = Disponil A3065 and TA = Disponil FES 32S

Table 2 Characteristics of miniemulsions created by SM

 2

	Parameter	MMA/BuA	MMA	BuA	ST
	 of Mini mN/m	9.4	3.6	7.6	10