Regional rainfall thresholds for landslide occurrence using a centenary database

Nat. Hazards Earth Syst. Sci., 18, 1037–1054, 2018 https://doi.org/10.5194/nhess-18-1037-2018 © Author(s) 2018. This work is distributed under the Creative Commons Attribution 4.0 License. Regional rainfall thresholds for landslide occurrence using a centenary database Teresa Vaz, José Luís Zêzere, Susana Pereira, Sérgio Cruz Oliveira, Ricardo A. C. Garcia, and Ivânia Quaresma Centre for Geographical Studies, Institute of Geography and Spatial Planning, Universidade de Lisboa, Lisbon, 1600-276, Portugal Correspondence: Teresa Vaz (tv[email protected]) Received: 12 October 2017 – Discussion started: 25 October 2017 Revised: 2 March 2018 – Accepted: 7 March 2018 – Published: 4 April 2018 Abstract. This work proposes a comprehensive method to assess rainfall thresholds for landslide initiation using a centenary landslide database associated with a single centenary daily rainfall data set. The method is applied to the Lisbon region and includes the rainfall return period analysis that was used to identify the critical rainfall combination (cumulated rainfall duration) related to each landslide event. The spatial representativeness of the reference rain gauge is evaluated and the rainfall thresholds are assessed and calibrated using the receiver operating characteristic (ROC) metrics. Results show that landslide events located up to 10 km from the rain gauge can be used to calculate the rainfall thresholds in the study area; however, these thresholds may be used with acceptable confidence up to 50 km from the rain gauge. The rainfall thresholds obtained using linear and potential regression perform well in ROC metrics. However, the intermediate thresholds based on the probability of landslide events established in the zone between the lower-limit threshold and the upper-limit threshold are much more informative as they indicate the probability of landslide event occurrence given rainfall exceeding the threshold. This information can be easily included in landslide early warning systems, especially when combined with the probability of rainfall above each threshold. 1 Introduction Rainfall is the most important physical process for landslide triggering in Portugal (Zêzere et al., 2015; Vaz and Zêzere, 2016) as well as worldwide (e.g. Crozier, 1986; Crosta and Frattini, 2008). However, the relationship between rainfall and landslides is indirect and typically includes a process cascade where the rainfall is followed by infiltration into the soil, which increases the pore-water pressure that is responsible for the decrease in the shear strength of the slope materials (Terlien, 1998; Glade and Crozier, 2005). During the last decades, the relationship between landslides and rainfall has been tentatively established by the assessment of rainfall thresholds, i.e. rainfall conditions (cumulated rainfall, intensity), that when reached or exceeded can induce a landslide event (Reichenbach et al., 1998; Guzzetti et al., 2007). The rainfall thresholds for slope failure have been proposed following a physical and empirical approach. The first approach considers the physical basis of the process using hydrological models and stability calculations (Terlien, 1998; Iverson, 2000; Frattini et al., 2009). However, it demands high-resolution data (e.g. groundwater conditions; shear strength properties) that often are not available for large areas (Guzzetti et al., 2007). The second approach is statistically based and is sustained by historical records regarding landslide events and rainfall data series (Guzzetti et al., 2007). Several thresholds have been proposed worldwide using the empirical approach, which can differ according to the kind of rainfall measurements and variables and the number of rain gauges used to calculate the threshold, as well as the geographical extent over which the threshold is applied. The most common empirical rainfall thresholds used at local and regional scales are the rainfall intensity and duration (I–D) threshold, the event duration (E-D) threshold, the antecedent rainfall threshold and the combined threshold. The I–D threshold links the total height of rainfall and the rainfall intensity (Caine, 1980) and has been widely used as a power-law threshold (e.g. Guzzetti et al., 2008; Saito et Published by Copernicus Publications on behalf of the European Geosciences Union. 1038 T. Vaz et al.: Regional rainfall thresholds for landslide occurrence using a centenary database al., 2010; Brunetti et al., 2010). It has shown good performance, especially for shallow landslides triggered by short and intense rainfall. Alternatively, the E-D threshold associates the cumulated-rainfall event with the rainfall event duration (e.g. Peruccacci et al., 2012). The antecedent rainfall thresholds assesses the influence of the antecedent rainfall on the groundwater levels and soil moisture, thus acting as a landslide preparatory factor. This is particularly important for deep-seated landslides induced normally by long-lasting rainfall periods (Martelloni et al., 2012). However, the definition of the critical rainfall period is an important source of bias for the antecedent rainfall (e.g. Guzzetti et al., 2007; Zêzere et al., 2015) and different periods have been proposed in the literature, ranging from a few days to several months (e.g. Glade et al., 2000; Cardinali et al., 2006). Finally, the combined thresholds include several combinations such as the rainfall event combined with rainfall intensity (e.g. Onodera et al., 1974), the event rainfall with the antecedent rainfall (e.g. Pereira and Zêzere, 2012), the event rainfall with the antecedent calibrated rainfall (e.g. Zêzere et al., 2005). The rainfall thresholds for landslide activity obtained in a study area cannot be extrapolated for other regions, namely because of changes regarding the climatic regime (Glade et al., 2000). To allow the comparison of rainfall thresholds obtained in different areas, rainfall data have been normalized using two climatic indices: the mean annual precipitation (MAP) (Cannon, 1988) and the rainy day normal (RDN) (Wilson, 1997). The different rainfall parameters can be divided by the two climatic indices to obtain, for instance, the normalized intensity duration (e.g. Wieczorek et al., 2000), the normalized event duration (e.g. Giannecchini, 2005) and the normalized antecedent rainfall (e.g. Aleotti, 2004). The rainfall measurements used to assess rainfall thresholds for landslide activity can be based on a single reference rain gauge (e.g. Zêzere et al., 2005; Marques et al., 2008; Martelloni et al., 2012) or on multiple rain gauges (e.g. Peruccacci et al., 2012). The close proximity, similar elevation and topographical and morphological settings are the preferable criteria with which to select the representative area of a rain gauge (Brunetti et al., 2010). However, the distance to where the rain gauge is spatially representative is a critical point that often is not addressed and can be an additional source of bias for the threshold definition, as pointed out by Nikolopoulos et al. (2015). The assessment of rainfall thresholds implies the consideration of two types of information that link rainfall and landslides in a single study area: the rainfall events that triggered landslides in a defined time period in the past and the rainfall events that did not trigger landslides in the same time period. Considering the rainfall data sets associated (and nonassociated) with landslide events two distinct rainfall thresholds can be defined: (i) the lower-limit threshold, which is the limit below which the landslides have not been recorded, and (ii) the upper-limit threshold, which is the limit above which landslides have always been recorded (Glade et al., 2000). The zone between the lower-limit and upper-limit thresholds includes rainfall conditions that triggered and did not trigger slope failures in the past. As a rule, the uncertainty increases with the gap between the lower-limit and upper-limit thresholds. Therefore, between the lower threshold and the upper threshold different probabilities of landslide occurrence exist that are important to quantify. The main purpose of this study is to present and discuss a comprehensive method to assess rainfall triggering thresholds using a centenary landslide database associated with a single centenary daily rainfall data set. In addition, five specific objectives are stated: (i) to identify the critical combinations of cumulated rainfall duration for landslide occurrence, (ii) to compute the antecedent rainfall thresholds using linear and potential regression and define the lower-limit and the upper-limit rainfall thresholds, (iii) to assess the thresholds performance using receiver operating characteristic (ROC) metrics, (iv) to estimate the probability of rainfall threshold and the probability of landslide events above a specific rainfall threshold, and (v) to identify the geographical area where the rainfall thresholds can be applied. 2 Study area and general characteristics of the rainfall regime The Lisbon region is located in the southern Portuguese Estremadura, which is divided into two parts by the Tagus River (Fig. 1). The landscape is marked by hills and valleys and three mountains of limited extension and altitude (Fig. 1): the Montejunto Mountain in the north-west (666m altitude), the Sintra Mountain in the west (528 m) and the Arrábida Mountain in the south (501 m). The climate in the Lisbon region, as in Portugal, is influenced by the subtropical anticyclone and the subpolar depression zone (Espírito Santo et al., 2014; Lima et al., 2015). The atmospheric general circulation combined with the orography and the oceanic and continental influences are the most important factors that shape the regional climate (Nunes and Lourenço, 2015). The rainfall regime is typically irregular, with an interannual and intra-annual variability (Kutiel and Trigo, 2014). The interannual variability is notorious in the centenary annual rainfall data registered at the Lisboa-Geofísico rain gauge (Fig. 2). The mean annual rainfall (MAR) is 709mm, but the variability is very high and wet years can be followed by severely dry years. In some climatological years the annual rainfall reached twice the MAR (e.g. more than 1400mm in 1876/1877), while other climatological years did not reach half of the MAR (e.g. less than 300 mm in 2004/2005). The intra-annual rainfall regime is characterized by seasonality (Fig. 3), with two important seasons (dry and wet) separated by transition periods (Ribeiro et al., 1999). During 2 months of summer (July and August) the rainfall is almost absent in quantity and frequency. On average, only Nat. Hazards Earth Syst. Sci., 18, 1037–1054, 2018 www.nat-hazards-earth-syst-sci.net/18/1037/2018/ T. Vaz et al.: Regional rainfall thresholds for landslide occurrence using a centenary database 1039 600 800 1000 600 800 600 600 600 600 600 600 600 800 800 Sintra Almada Lisbon Setúbal Cascais Arrábida Montejunto 8°40' W9° W9°20' W9°40' W 39° N 38°40' N 38°20'N 0 20 km 0 200 km Elevation (m) Tagus River Sado River ! (Lisboa-Geofísico rain gauge Mean annual rainfall (mm) [0–25[ [25–50[ [50–100[ [100–150[ [150–200[ [200–250[ [250–300[ [300–350[ [350–400[ [400–450[ [450–500[ [500–550[ [550–600[ [600–660] Figure 1. Elevation and mean annual rainfall in the study area (source: Daveau et al., 1977). 1.3 % of the annual rainfall is concentrated in these months. The Azores anticyclone influence, in its north-westerly position, explains the warm and dry air that affects the Lisbon region during this season (Trigo and DaCamara, 2000). The monthly rainfall is highest from October to March, but with a strong interannual variability. On average, this period concentrates more than 75 % of the annual rainfall, with a frequent peak in November. This wet period is explained by the large-scale circulation led by the Icelandic low-pressure system, which brings moist air responsible for rainfall events (Trigo and DaCamara, 2000). September, April, May and June are transition months and can be highly variable from one year to another concerning the amount of rain. As a rule, the types of weather circulation, associated with high rainfall amounts, are of cyclonic and westerly type (Trigo and DaCamara, 2000; Ramos et al., 2014). Recently, it was found that the winter storms in Europe, responsible for large amounts of precipitation, have a tendency to cluster temporally (Mailier et al., 2006; Vitolo et al., 2009; Pinto et al., 2013). Therefore, storms with high magnitude are followed by other storms, increasing the probability of inducing other natural hazards, such as floods and landslides. 3 Data and methods 3.1 Identification of landslide events The landslide database used in this study includes the DISASTER database and has detailed information about the date and location of landslide occurrence. The DISASTER database was carried out by exploring several daily and weekly newspapers, published in Portugal between 1865 and 2010, which include all the landslides that caused fatalities, injuries, missing people, evacuated and homeless people. The method used to construct the DISASTER database has been widely described and can be found in Zêzere et al. (2014). Additionally, using the same newspaper sources, landslides that did not cause any human damage during the same time period were identified and included in the database that supported this study. It should be pointed out that falling walls and instabilities directly resulting from engineering works were rejected. Similarly, the landslides in active coastal cliffs were not included in the database. The database structure is divided into two sections: landslide features and landslide damages. The first section includes information on landslide type, temporal and spatial location, trigwww.nat-hazards-earth-syst-sci.net/18/1037/2018/ Nat. Hazards Earth Syst. Sci., 18, 1037–1054, 2018 1040 T. Vaz et al.: Regional rainfall thresholds for landslide occurrence using a centenary database 0 200 400 600 800 1000 1200 1400 1600 1800 2000 1864/65 1868/69 1872/73 1876/77 1880/81 1884/85 1888/89 1892/93 1896/97 1900/01 1904/05 1908/09 1912/13 1916/17 1920/21 1924/25 1928/29 1932/33 1936/37 1940/41 1944/45 1948/49 1952/53 1956/57 1960/61 1964/65 1968/69 1972/73 1976/77 1980/81 1984/85 1988/89 1992/93 1996/97 2000/01 2004/05 2008/09 Rainfall (mm) MAR Figure 2. Annual rainfall (climatological year: September to August) at Lisboa-Geofísico rain gauge for the period 1864/1865–2009/2010. Orange line symbolizes the mean annual rainfall (MAR); red dots and back triangles symbolize rainfall-triggered landslide events and nonrainfall-triggered landslide events, respectively, at a distance up to 10 km from the reference rain gauge. 0 50 100 150 200 250 300 350 400 450 500 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Rainfall (mm) P10 P20 P30 P40 P50 P60 P70 P80 P90 Figure 3. Monthly rainfall percentiles at Lisboa-Geofísico rain gauge for the period 1864/1865–2009/2010. Brown dots and grey triangles symbolize the 30-day cumulated absolute antecedent rainfall for the rainfall-triggered landslide event and for the non-rainfall-triggered landslide event, respectively, at a distance up to 10 km from the reference rain gauge. gering factors and newspaper metadata. The second section refers to the human consequences of landslides (fatalities, injuries, missing people, evacuated and homeless people), and direct and indirect damage to buildings, structures, roads and railroads. Our analysis is focused on the dates of landslide occurrences. The newspapers are a reliable data source, despite the existing uncertainty concerning the spatial location of many reported landslide events, as well as on their type. Only landslides with at least 1 day of accuracy were included in the database. The spatial accuracy of landslide cases was divided into five classes, following Zêzere et al. (2014): (i) locations with the exact coordinates (accuracy associated with scale 1 :1000), (ii) locations based on local toponymy (accuracy associated with scale 1 :10000), (iii) locations based on local geomorphology (accuracy associated with scale 1 :25000 scale), (iv) locations in the centre of the parish and (v) locations in the centre of the council. A total of 400 landslide cases were inventoried, with the majority (83 %) located with accuracy corresponding to classes (i) to (iii). These landslides affected clay (40.24 %), sandstone and conglomerate (22.52 %), limestone (16.52 %), volcanic (11.11 %), marly and marly limestone (9.01 %) and granite (0.60 %). The landslide type was classified following the Cruden and Varnes (1996) classification scheme. Slides are the dominant landslide type in the database (53.8 %), followed by falls (14.4 %). Flows and complex slope movements are less representative (2.4 and 1.5%, respectively). Nat. Hazards Earth Syst. Sci., 18, 1037–1054, 2018 www.nat-hazards-earth-syst-sci.net/18/1037/2018/ T. Vaz et al.: Regional rainfall thresholds for landslide occurrence using a centenary database 1041 The landslide type is unknown in 27.9 % of the cases. In this study the analysis was performed for all landslide types, following the approach of similar studies (e.g. Brunetti et al., 2010; Rosi et al., 2012; Peruccacci et al., 2017). 3.2 Selection of rain gauge and identification of critical rainfall combinations In this study the following definition was adopted for landslide events: an individual landslide or a set of landslides that occurred on a precise date (day). In those cases where the activity period of a landslide was reported as lasting several days, the first day of the period was considered for the landslide event. The selection of the reference rain gauge took into account the available time series, the data quality and resolution and the climatic representativeness. The daily rainfall data were collected at the Lisboa-Geofísico rain gauge (latitude 38.72◦N, longitude 9.15◦W, elevation 77m), located within the city of Lisbon. The rainfall daily measurements at Lisboa-Geofísico started in 1864 and is one of the few rain gauges with centennial-long daily records in Portugal. A long time series of rainfall data is an important condition for creating comprehensive thresholds based on the analysis of the rainfall return period. In addition, this rain gauge presents reliable data, the quality and completeness of which was already tested and confirmed by Kutiel and Trigo (2014). The rainfall measurements have been taken without interruption and always in the same place since 1864. Furthermore, the rain gauge is climatically representative of the Lisbon region, with a rainfall regime influenced mainly by the atmospheric general circulation and the oceanic proximity. The daily rainfall refers to the period between 09:00UTC on the previous day and 09:00 UTC on the day of measurement, whereas the landslide dates are ascribed to a period from 00:00 to 23:59UTC. Due to this difference, the date of each landslide event reported by the newspaper was compared with the daily rainfall registered in 3 days (from the day before up to the day after), and the day registering the highest rainfall amount was selected as the day of the landslide event. The reconstruction of cumulated rainfall follows the method proposed by Zêzere et al. (2005). In a first step, the daily rainfall data registered at the Lisboa-Geofísico rain gauge during the period 1864/1865–2009/2010 were organized by climatological year (September to August). The decision to use the climatological year instead of the hydrological year (October–September) is justified by the rainfall regime of the study area. Starting the analysis in September, after the month with the low values of rainfall (August), we capture the complete transition period towards the wet season in each year. Afterwards, for each day, from 1864 to 2010 the cumulated antecedent rainfall was calculated for the durations of 1, 2, 3, 4, 5, 10, 15, 20, 30, 40, 50, 60, 75 and 90 days. The maximum annual records of daily rainfall and cumulated rainfall for each duration were extracted and analysed using the theoretical distribution described by Gumbel (1958). This distribution is also known as the distribution of Fisher–Tippett and is applied to the extreme values. With the Gumbel law it is possible to obtain the probability of occurrence of each rainfall value within the series with Nvalues. The reduced Gumbel distribution (y) is calculated with Eq. (1): y= −ln−ln m N+1,(1) where mis the position number of the respective observations and Nis the total number of observations. Considering this distribution, the theoretical frequencies can be calculated by the average and standard deviation for the reduced Gumbel distribution (My and Sy) and for the rainfall values (Mx and Sx). Eq. (2) expresses the theoretical trend: y=α(x −µ), (2) where yis the reduced variable and xthe rainfall value. The parameters αand µare calculated as follows: 1/α =Sx/Sy (3) µ=Mx −My/α. (4) Finally, the probability of exceedance of any rainfall value is given by the Eq. (5): P (x) =1−e−e−y.(5) For each landslide event the cumulated antecedent rainfall was assessed for the durations of 1, 2, 3, 4, 5, 10, 15, 20, 30, 40, 50, 60, 75 and 90 days. For each antecedent rainfall the return period (RP) was calculated with Eq. (6): RP =1 1−e−e−y.(6) The pair (cumulated rainfall duration) with the highest return period was considered to be the critical rainfall combination, responsible for triggering the landslide event. This assumption is not physically based, but has been applied in previous work (e.g. Marques et al., 2008; Zêzere et al., 2008, 2015) and provides the best discrimination of the rainfall events related to landslide activity (Zêzere et al., 2005). Moreover, this approach agglomerates the rainfall that triggered the landslide event and the antecedent rainfall that contributed as a landslide preparatory factor. As was previously mentioned, our landslide database was collected from newspaper sources and in some cases the rainfall triggering is not clear. Therefore to calculate the threshold we decided to use only the landslide events which have a critical rainfall combination with a return period exceeding 3 years. The boundary is arbitrary, but this criterion reduces the possibility of considering landslide events with a www.nat-hazards-earth-syst-sci.net/18/1037/2018/ Nat. Hazards Earth Syst. Sci., 18, 1037–1054, 2018 1042 T. Vaz et al.: Regional rainfall thresholds for landslide occurrence using a centenary database triggering factor other than rainfall (e.g. human action). The landslide events associated with critical rainfall combinations with return period less than 3 years were assumed to not be triggered by rainfall. Finally, the climatological years without landslide records in the database were selected and the maximum yearly cumulated rainfall was identified for durations lasting from 1 to 90 consecutive days. These data were further used as rainfall events that did not generate landslide events and are crucial for the thresholds definition and calibration. 3.3 Critical distance from the rain gauge The critical distance where the rain gauge is regionally representative was evaluated by drawing several buffers up to 60 km from the rain gauge (5, 10, 15, 20, 30, 40, 50 and 60 km). The ratio between the non-rainfall-triggered landslide events and the rainfall-triggered landslide events within each buffer was used to identify the area where the rain gauge is representative. During the analysed time period (1864/1865–2009/2010) landslides in the study area were mostly triggered by rainfall and the earthquake trigger can be neglected (Vaz and Zêzere, 2016). The human action was an additional landslidetriggering factor, in particular through artificial cuts and drainage constraints associated with the progressive enlargement of urban areas. As it was already mentioned, the reference rain gauge is located in the city of Lisbon, where the landslides induced by human action are expected to be higher in number when compared with the outside of the urban area. Following this assumption, the ratio between the non-rainfall-triggered landslide events and the rainfalltriggered landslide events should decrease as the distance from the gauge increases. If this relation does not occur we assume that the rain gauge is no longer representative for the corresponding buffer. Therefore, the lowest ratio between non-rainfall-triggered landslide events and rainfall-triggered landslide events was considered to define the critical distance where the rain gauge is regionally representative to assess rainfall thresholds for landslide occurrence. 3.4 Rainfall triggering thresholds assessment and calibration Landslide events registered within the critical distance from the rain gauge were considered and rainfall thresholds were established using linear and potential regression, based on cumulated rainfall duration with the highest return period. The lower-limit and the upper-limit rainfall thresholds were also defined following the suggestion by Glade et al. (2000). The lower-limit and the upper-limit rainfall thresholds were defined by linear regression based on two pairs. The lower limit was established by iteratively selecting two landslide events associated with different durations with the lowest values of cumulated critical rainfall and ensuring that the complete set of landslide events fall above the threshold. The upper limit was established by iteratively selecting the two highest pairs (cumulated rainfall/duration) that did not trigger landslides and ensuring that the complete set of nonlandslide events fall below the threshold. When representing thresholds we avoid using logarithm scales, and thresholds were established as linear relationships instead of using a power law, with a single exception (the potential regression threshold). These options maximize the zone between the lower-limit and upper-limit thresholds, thus allowing the distinction between rainfall events that generated (did not generate) landslide events. The performance of rainfall thresholds was evaluated using ROC metrics. ROC analyses are commonly used to validate susceptibility landslide models (Beguería, 2006; Kappes et al., 2011) and it is based on confusion matrices. The principles used in these analyses can also be applied to calibrate the rainfall thresholds (e.g. Staley et al., 2013; Gariano et al., 2015a; Zêzere et al., 2015). The confusion matrix is used to assess the correct and incorrect predicted observations, for positive and negative cases (Beguería, 2006). Therefore, the analysis is based on the evaluation of true positive (TP), false negative (FN), true negative (TN) and false positive (FP) cases. When applied to rainfall thresholds the TP corresponds to the landslide events in which the rainfall combination (cumulated rainfall duration) is above the threshold. The FN are landslide events for which the rainfall combination (cumulated rainfall duration) is below the threshold. The rainfall combinations that did not resulted in landslide events are classified as TN if they are below the threshold or FP if they are above the threshold. Also, four ROC metrics functions described by Staley et al. (2013) were used in this study (Table 1). The true positive rate (TPr)is the proportion of landslide events that were correctly predicted by the threshold (Table 1). The false positive rate (FPr)is the proportion of rainfall events above the threshold for which there is no information on landslide occurrence. The false alarm rate (FAr)is the ratio between false predictions and the complete set of rainfall events above the threshold. The threat score (TS) is used to evaluate the threshold to maximize the number of correct predictions while minimizing the rate of FP and FN. A TS=1 represents a perfect model but is reduced by incorrect predictions. The probability of a rainfall event above the rainfall threshold resulting in a landslide event was measured by the positive predictive rate (PPr), which was previously described by Bradley (1997) and Fawcett (2006). The PPrmeasures the relationship between the rainfall events above the threshold that resulted in landslide events and the complete set of rainfall events located above the threshold, as follows: PPr=TP TP +FP.(7) Nat. Hazards Earth Syst. Sci., 18, 1037–1054, 2018 www.nat-hazards-earth-syst-sci.net/18/1037/2018/ T. Vaz et al.: Regional rainfall thresholds for landslide occurrence using a centenary database 1043 Table 1. ROC metrics (according to Staley et al., 2013). Formulation Optimal value True positive rate (TPr)TPr=TP TP+FN 1 False positive rate (FPr)FPr=FP FP+TN 0 False alarm rate (FAr)FAr=FP TP+FP 0 Threat score (TS) TS =TP TP+FN+FP 1 Therefore, the PPris the opposite of the FArand can also be calculated by the expression: PPr=(1−FAr). (8) Using this approach, several linear rainfall thresholds were plotted in the zone between the lower-limit and the upperlimit rainfall thresholds, and the corresponding PPrwere calculated in order to compute the probability of landslide events associated with each threshold. In addition, the probability of each rainfall threshold was computed based on the return period of the corresponding cumulated rainfall duration. Lastly, the performance of the lower-limit threshold was assessed beyond the critical distance of the rain gauge. For each buffer referred to in Sect. 3.2 the ratio between the FN and the total set of landslide events (TP+FN) was systematically evaluated. We assume the lower-limit threshold can only be applied to those buffer distances where this ratio remains stable. 4 Results 4.1 Landslide events and critical distance from the rain gauge Within the area located up to 60 km from the reference rain gauge 223 landslide events were identified dating from 1865 to 2010 (Fig. 4). However, the return period computed for the cumulated rainfall does not exceed 3 years in 92 landslide events. Therefore, according to the criterion defined in Sect. 3.2, these landslide events were assumed not to have been triggered by rainfall. The ratio between the number of non-rainfall-triggered landslide events and the number of rainfall-triggered landslide events was calculated for each buffer zone shown in Fig. 4. The results are summarized in Table 2 and were used to define the critical distance at which the rain gauge is regionally representative, and to select the landslide events considered to compute the rainfall thresholds. We acknowledge the ratio differences that occurred only to the second 10 km 60 km 50 km 40 km 30 km 20 km 15 km 5 km 8°40'W9° W9°20' W9°40' W 39° N 38°40' N 38°20' N 0 20 km ! (Lisboa-Geofísico rain gauge Landslides ! ( Figure 4. Distribution of landslides in the Lisbon region (1865/2010) and buffer distances from the reference rain gauge. decimal place (Table 2), but these differences can be interpreted considering the characteristics of the study area. Within the 5 km buffer the calculated ratio is relatively high (0.65). The first buffer zone includes Lisbon city centre, which explains the high number of landslides triggered by factors other than rainfall, mainly due to human actions. In the following buffer zone (10km) the ratio decreases to 0.63. This decrease was expected as the urban area extension decreases in the second buffer, thus justifying the lower number of non-rainfall-triggered landslides. The ratio between the non-rainfall-triggered and the rainfall-triggered landslide events increases to 0.66 within the 15km buffer zone, and the ratio ranges between 0.66 and 0.70 in the next buffer zones up to 60km from the rain gauge. The increasing ratio in distance exceeding 10km from the rain gauge cannot be attributed to the occurrence of an unexpectedly high number of non-rainfall-triggered landslide events, but can only be explained by a decrease in spatial representativeness of the rain gauge data in areas beyond 10 km. Therefore, we consider 10km the critical distance at which the rain gauge is representative, and the rainfall thresholds were computed considering only the landslide events registered within this zone. In the area located up to 10 km from the reference rain gauge of Lisboa-Geofísico 60 landslide events, with return periods below 3 years, were assumed to be non-rainfalltriggered landslides, and therefore were not considered for the threshold calculation and analysis. Moreover, 96 rainfallwww.nat-hazards-earth-syst-sci.net/18/1037/2018/ Nat. Hazards Earth Syst. Sci., 18, 1037–1054, 2018 1044 T. Vaz et al.: Regional rainfall thresholds for landslide occurrence using a centenary database Table 2. Ratio of non-rainfall-triggered landslide events/rainfall-triggered landslide events for different buffer distance to the reference rain gauge. Distance to the Non-rainfall-triggered Rainfall-triggered Ratio (a/b) rain gauge (km) landslide events (a) landslide events (b) 5 51 78 0.65 10 60 96 0.63 15 67 101 0.66 20 69 105 0.66 30 78 117 0.67 40 86 125 0.69 50 88 128 0.69 60 92 131 0.70 triggered landslide events were identified, which include 187 individual landslides. The yearly and monthly distributions of these landslide events are shown in Figs. 2 and 3, respectively. The rainfall-triggered landslide events occurred mainly in wet years: 89% of landslide events were registered in years with rainfall above the MAR. The climatological years 1876/1877, 1946/1947 and 1968/1969 are in the top regarding the number of landslide events (six events in each year). In these three climatological years the annual rainfall was above 933mm at the reference rain gauge, which exceeds the MAR by more than 30 %. However, there is not a direct relationship between the MAR and landslide events because landslide occurrence is usually related to rainfall events over a few days or weeks, which are not expressed by the mean annual rainfall. Indeed, landslide events were also registered in 10 years with annual rainfall below MAR, as was the case for 1909/1910, which registered two landslide events. The monthly distribution of landslide events follows the rainfall distribution over the year in a Mediterranean climate, with dry summers and wet winters. The landslide events essentially coincide with most rainy months, as 92% of events occurred from November to March. Within this period, January and February stand out with the highest concentration of landslide events (24 and 22.9%, respectively). Besides the monthly rainfall percentile, Fig. 3 represents the 30day cumulated antecedent rainfall for each landslide event and shows that 96 % of landslide events are above the 70th percentile. If we consider the 90th percentile this value decreases to 79%, but it continues to highlight the exceptionality of rainfall during the 30 days before the landslides are triggered. For each landslide event the critical cumulated rainfall duration was obtained following the method described in Sect. 3.2. The obtained critical durations associated with landslide events range from 1 to 90 consecutive days. The monthly distribution of critical durations is shown in Fig. 5 for the rainfall-triggered landslide events. The shorter rainfall events (less than 20 consecutive days) occurred mainly from September to December (56 %) at the beginning of the rainy 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 10 15 20 30 40 50 60 75 90 % Consecutive days May Mar Feb Jan Dec Nov Oct Sep Figure 5. Monthly frequency of the rainfall-triggered landslide events against the duration of the rainfall period. period. On the contrary, when associated with longer rainfall periods (more than 20 consecutive days) the landslide events were more frequent from January to May (86 %). Figure 6 illustrates the cumulated rainfall duration combinations that resulted in landslide events and the typical return periods established for 3, 5, 10, 25, 50, 100, 150 and 200 years. Around 64% of the cumulated rainfall duration that resulted in landslide events have a return period below 10 years. However, four landslide events had a rainfall amount and duration with a very high return period, above 150 years. Figure 6 also identifies the landslide events that include multiple landslides and the landslide events that are constituted by a single landslide. The distribution of both groups is inconclusive, as the landslide events containing multiple landslides are not always directly related to the exceptionality of the rainfall event, i.e. the critical cumulated rainfall duration combination with a higher return period. 4.2 Rainfall thresholds for landslide triggering The rainfall conditions (cumulated rainfall duration) associated with each landslide event were considered to define rainfall thresholds using linear and potential regression (Fig. 7). The linear regression follows the equation R=5.5D+124.6, where Dis the duration in days, whereas the potential regression follows the equation R=67.8D0.46 (Table 3). The coefNat. Hazards Earth Syst. Sci., 18, 1037–1054, 2018 www.nat-hazards-earth-syst-sci.net/18/1037/2018/ T. Vaz et al.: Regional rainfall thresholds for landslide occurrence using a centenary database 1045 0 100 200 300 400 500 600 700 800 900 1000 010 20 30 40 50 60 70 80 90 Rainfall (mm) Consecutive days Single landslides Multiple landslides Non-rainfall-triggered landslide events Figure 6. Critical combination cumulated rainfall duration that resulted in landslide events (single and multiple landslides) and return period (RP) for 3, 5, 10, 25, 50, 100, 150 and 200 years. Distance up to 10km from the reference rain gauge. The non-rainfall-triggered landslide events identified are also represented. ficient of determination is very high in both cases (R2=0.8 and 0.9, respectively). Both rules can be used as rainfall thresholds for landslide occurrence in the study area; however none of them ensure a low number of false negative occurrences (i.e. landslide events below the threshold). To calibrate the thresholds, the maximum yearly rainfall for each duration (1 to 90 consecutive days) was calculated for those climatological years without records of landslide events in the analysed period (1865–2010). These records represent rainfall events not associated with landslides and are symbolized by grey dots in Fig. 7 (1428 dots). The majority of these rainfall events (96.6 %) drop below the threshold obtained with the potential regression. However, there are 57 false negatives occurrences (i.e. events that occurred without being predicted), as well as 48 false positives (i.e. rainfall events lying above the threshold, without any landslide reported). In the next step, the lower-limit and the upper-limit rainfall thresholds were determined. The former establish the threshold below which there are no true positives (landslide events), whereas the latter establish the threshold above which there are no false positives (rainfall events without landslides). The lower-limit threshold follows the equation R=4.4D+56.5, and the upper-limit threshold follows the equation R=7.3D+235.8, where Dis the duration in days (Table 3). Table 3 also summarizes the ROC metrics for the regression thresholds (linear and potential) and the lower-limit and the upper-limit thresholds. The TPrmeasure the proportion of landslide events that occurred when the combinations of rainfall duration are exceeded and show the efficiency of a threshold to predict a landslide event. On the other hand, the FPrmeasures the proportion of combinations of rainfall duration that are above the threshold but did not result in any known landslide event. For the potential regression threshold, the TPris not very high (0.41, best value is 1) but the FPris a good result (0.03, the best value is 0), which means that the thresholds have a low probability of a false detection. The TPris equal to 1 for the lower-limit threshold, considering that it was drawn to avoid FN occurrences. However, the FPrand the FArare very high (0.37 and 0.85, respectively) as a consequence of the typical low values of the threshold. The lower limit is a conservative threshold, and its main advantage is predicting all the landslide events, but it also includes a very high number of false positive events. On the contrary, the upper-limit threshold is only surpassed by true positive occurrences, so the FPrand FArhave the best result (0 value). However, the TPris very low (0.03) reflecting the high number of false negative events. The threat score (TS) provides a better understating of each threshold performance as it relates to the TP, FN and FP occurrences. 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