Temporal patterns of nonseismically triggered landslides in Shaanxi Province, China

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Temporal patterns of nonseismically triggered landslides in Shaanxi Province, China ⁎

Haijun Qiua,b,c, , Yifei Cuid, Yanqian Peic, Dongdong Yangc, Sheng Huc, Xingang Wange, Shuyue Mac a

Shaanxi Key Laboratory of Earth Surface System and Environmental Carrying Capacity, Northwest University, Xi’an 710127, China Institute of Earth Surface System and Hazards, Northwest University, Xi’an 710127, China c College of Urban and Environmental Sciences, Northwest University, Xi’an 710127, China d State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 10084, China e State Key Laboratory of Continental Dynamics, Department of Geology, Northwest University, Xi'an 710069, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Historical landslides Temporal patterns Time series Rainfall Shaanxi Province

Examination of the temporal patterns of landslide events provides valuable insights into the baseline information used to determine landslide activity and perform risk assessment in a given area. We collected a catalog of historical nonseismically triggered landslides that occurred over 22 years in Shaanxi Province, China. We found that the annual number of slides was significantly related to the annual number of falls. The average annual numbers of slides and falls were approximately 17 and 10, respectively. The active and nonactive periods of landslides alternated within the time series of the annual number of landslides. An empirical power-law correlation exists between the complementary cumulative frequency and the annual number of landslides. The monthly distribution of landslide events is significantly associated with monthly rainfall. Most landslide events occurred in the rainy season between July and October. The average time intervals of falls and slides from July to October were approximately 12 days and 8 days, respectively. Moreover, the temporal distribution of landslide events is clustered owing to the impact of nonuniformly distributed rainfall activities. Most of the landslides concentrated in one or two months of a year. Furthermore, the nonzero values in the landslide time series are nonuniformly spaced. The complementary cumulative frequency distribution of the time intervals between landslide events can be adequately fitted by an exponential function. Based on these equations, the temporal probabilities of landslide events can be predicted. In addition, most of the nonseismically triggered landslides in Shaanxi Province were triggered by long-term antecedent rainfall and high-intensity intraday rainfall.

1. Introduction

2011; Qiu et al., 2018b). Knowledge of the temporal patterns of landslide occurrence in a given geographic area is especially important for landslide hazard assessment, the establishment of effective landslide warning systems, and the estimation of landslide erosion rates (González-Dı́ez et al., 1999; Harmon and Doe, 2001; Aleotti, 2004; Korup, 2005; Keefer and Larsen, 2007; Guzzetti et al., 2009; Rossi et al., 2010). A considerable number of studies have investigated the spatial distribution of landslides and its relation to various environmental conditions (Dai et al., 2011; Collins et al., 2012; Zhang et al., 2014; Bandara and Ohtsuka, 2017; Martha et al., 2017). Time series are employed in many disciplines (Witt and Malamud, 2013), and some authors have provided a temporal analysis of landslide events and fatality data (Guzzetti et al., 2005; Petley, 2012; Tanyaş et al., 2017; Froude and Petley, 2018; Zhang and Huang, 2018).

Landslides are recognized in many parts of the word as major natural hazards due to their substantial destructive impacts on the environment and society (Nadim et al., 2006; Kirschbaum et al., 2010; Petley, 2012; Samia et al., 2017; Cui et al. 2019). Shaanxi Province in China has an extremely high exposure to landslide hazards due to its unique geomorphologic, geologic and climatic characteristics (Derbyshire, 2001; Huang and Li, 2011; Li et al., 2016; Qiu et al., 2016, 2018a; Zhuang et al., 2018). Landslides in this area are responsible for considerable economic losses and casualties (Zhang and Huang, 2018; Peng et al., 2019). In particular, because of the increasing population, rapid urbanization and economic pressures in Shaanxi Province, the impacts of landslides on human beings are increasing (Wang et al.,

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Corresponding author at: Shaanxi Key Laboratory of Earth Surface System and Environmental Carrying Capacity, Northwest University, Xi’an 710127, China. E-mail address: [email protected] (H. Qiu).

https://doi.org/10.1016/j.catena.2019.104356 Received 11 December 2018; Received in revised form 2 November 2019; Accepted 7 November 2019 0341-8162/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Haijun Qiu, et al., Catena, https://doi.org/10.1016/j.catena.2019.104356

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However, little attention has been devoted to the temporal patterns of landslide occurrence (Paudel et al., 2007; Rossi et al., 2010; Petley et al., 2005, 2012; Valenzuela et al., 2017). Landslide inventory is considered an essential and powerful tool for addressing landslide problems (Malamud et al., 2004; Guzzetti et al., 2012). Some researchers have presented global landslide catalogs based on local newspaper archives, media reports, scientific literature, historical archives, and other sources (Petley, 2012; Tanyaş et al., 2017; Kirschbaum et al., 2015; Piacentini et al., 2018). However, landslide information widely differs in terms of accuracy, level of completeness, quality of reporting and data availability (Kirschbaum et al., 2015; Tanyaş et al., 2017). In particular, little information regarding the date of occurrence of landslide events is given in many landslide inventories that cover long periods and large areas (Ibsen and Brunsden, 1996; Dikau and Schrott, 1999; Guzzetti and Tonelli, 2004; Rossi et al., 2010; Kirschbaum et al., 2015). Thus, it is necessary to ascertain the temporal distribution of landslides based on a detailed landslide inventory. In the current study, landslide catalogs were first collected by analyzing existing catalogs of historical landslide events, the Yearbook of Disaster Prevention, local historical archives and chronicles. The specific objectives of this research were to analyze the monthly and yearly temporal characteristics of historical landslide events, determine the frequency of the annual number of landslides, quantify the temporal concentration of landslide events, examine the time series of landslide events, study the complementary cumulative frequency of the time intervals between landslide events, and compare the temporal distributions between falls and slides. 2. Study area Shaanxi Province occupies an area of 2.05 × 105 km2 in northwestern China (Fig. 1) (Chen et al., 2015; Wu and Qian, 2017) and is predominantly characterized by rugged terrain. The area with a slope gradient greater than 25° accounts for 38% of the total area. The elevation in the province ranges from 170 m to 3767 m, with an average elevation of 1127 m (Liu et al., 2013). The study area is drained by the Yellow River and Han River and their major tributaries. The annual volume of water runoff is 4.26 × 1010 m3. The land use in this area is characterized by forests, croplands, pastures, orchards, urban areas and water (Chen et al., 2015; Cui et al., 2019). Shaanxi Province stretches from the southern Qinba Mountains to the northern Loess Plateau (Wu and Qian, 2017). The Wei River Valley lies between the Loess Plateau and the Qinba Mountains. The climate varies from north to south because of the large latitudinal span (Zhou and Van Rompaey, 2009; Wu and Qian, 2017). The annual mean temperature varies from 6.5 °C to 16.6 °C (Wu and Qian, 2017), and the mean annual rainfall is 576.9 mm. The northern Loess Plateau has a cold and arid or semiarid climate. This area is covered by thick loess and has the highest soil erosion in the world (Qiu et al., 2017). The landforms are characterized by loess-covered hills, loess-mantled ridges, and loess platforms (Liu, 1985). Loess landslides in this area are very widespread and play an essential role in the geomorphological evolution (Xu et al., 2012; Zhuang et al., 2018). The Wei River Valley climate is mostly semihumid. This area is the major region of industry, agriculture, and commerce in Shaanxi Province (Lu et al., 2010). The Qinba Mountains are much more humid and have a humid subtropical climate (Chen et al., 2015; Wu and Qian, 2017). This area lies in an active tectonic setting with considerable thrusts, faults, and folds. The steep topography, active tectonics, and intensive rainfall result in a susceptibility to landslides (Qian et al., 2015; Qiu et al., 2019a). Shaanxi Province is prone to considerable natural hazards due to active tectonics and locally intense rainfall (Liu et al., 2013). Approximately 70% of the annual rainfall occurs in the rainy season between May and September, consequently resulting in considerable landslides during this season, causing both severe damage to the regional economy and injuries to the local population (Zhuang et al.,

Fig. 1. Study area with identified landslide locations from 1996 to 2017 in Shaanxi Province, China.

2018). The main types of geohazards are slides, falls and debris flows. Some examples of catastrophic landslides in Shaanxi Province, China, are those that occurred on October 6, 2006, in Hua County, September 17, 2011, in Lantian County, and 12 August 2015 in Shanyang County (Zhuang and Peng, 2014; Qiu et al., 2019a). In particular, the Shanyang landslide was responsible for 65 casualties. As shown in Fig. 1, falls are likely to occur in the Loess Plateau, and debris flows are likely to occur in the Qinba Mountains. It has been observed that most landslides occur close to rivers, in cropland and grassland (Qiu et al., 2018b). 3. Materials and methods 3.1. Landslide catalogs Landslides are very common in Shaanxi Province. Fig. 2 shows four typical roadside landslides in the study area. Unlike other natural hazards, landslide events are generally not monitored by instrumentation (Rossi et al., 2010). Therefore, it is very difficult to obtain a consistent and complete record of landslide events over time (Ibsen and Brunsden, 1996; Guzzetti et al., 2000; Guzzetti and Tonelli, 2004; Rossi et al., 2010; Zhang et al., 2012; Jiang et al., 2016). Here, we developed a detailed catalog of historical nonseismically triggered landslides to construct a landslide time series by analyzing the Shaanxi Province Yearbook of Disaster Prevention released by the local government. The yearbook provides the geographical location, nearest populated place, type, and date of occurrence of the landslides and the economic losses and fatalities associated with the landslides. The advantage of this yearbook is that it is authoritative and 2

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Fig. 2. Typical landslide photos. (A) The landslide at location 110°15′23″; 35°1′19″. (B) The landslide at location 108°2′27″; 33°19′46″. (C) The landslide at location 108°42′14″; 36°52′27″. (D) The landslide at location 108°44′51″; 36°34′20″.

modified by Hungr et al. (2014), most of the observed landslides are either falls or slides. There are few debris flows, with insufficient data for statistical analysis. Hence, this study focused on an analysis of the falls and slides. In total, we exploited information on 591 nonseismically triggered landslides in Shaanxi Province for the 22-year period from 1996 to 2017; these events consisted of 212 falls and 379 slides. The information in the catalog includes the site number, type, geographical location, nearest populated place and date of occurrence of each reported landslide. The 5 unique fields in this catalog are summarized in Table 1. The locations of individual landslides are denoted by latitude and longitude coordinates. The accuracy of the geographical location information was sufficient for these analyses because the current study focuses on the temporal distribution rather than precise location information. Generally, determining the date of a landslide occurrence based on remote sensing interpretation and fieldwork is challenging for earth scientists (Carrara et al., 2003). The reliability of all documented information was evaluated for temporal precision. Based on validation and cross-checking, we found that the historical records in this yearbook accurately document the dates of landslide occurrences. Notably, the historical catalogs provide a minimum number of nonseismically triggered landslides occurring in Shaanxi Province. The statistical results from the landslide catalogs obtained here provide useful threshold values in the study area. For example, the time interval between landslide events in nature should be smaller than those

reliable. District offices in government departments must report every landslide event to their superior department according to the disaster relief system in place in China. The Department of Natural Resources of Shaanxi Province collects landslide information for publication in the Shaanxi Province Yearbook of Disaster Prevention. Additionally, local administrators commonly evaluate the impact of landslides based on the catalogs provided in the yearbook. Nonetheless, the yearbook still has disadvantages such as those related to data completeness. Data on landslides that affected infrastructure, resulted in casualties and were located near roads, villages, and towns were preferentially collected. Therefore, a yearbook does not report every landslide that occurred in the corresponding area over the corresponding period. In fact, complete catalogs of the temporal patterns of landslide occurrences over long periods are not available. The landslide catalogs that are obtained are meaningful and necessary for investigation because such landslide events can considerably affect human lives and are our primary concern. The catalogs can be valuable for estimations of human and economic losses and evaluation of emerging landslide prediction efforts (Kirschbaum et al., 2010; Petley, 2012). The biases and uncertainties in cataloging methods have been discussed in previous studies (Petley et al., 2005; Kirschbaum et al., 2010, 2015). The Shaanxi Province Yearbook of Disaster Prevention represents a continuous and systematic source landslide information. Therefore, most of the landslide data used in this study are collected from the Shaanxi Province Yearbook of Disaster Prevention. Furthermore, we used other data sources such as newspapers, literature, scientific reports, historical archives, and records from China’s Geological Environment Information Site (CGEIS, 2017) and the Department of Land and Resources of Shaanxi Province to validate and cross-check the data from the Shaanxi Province Yearbook of Disaster Prevention. We found that the information for a certain landslide from various data sources is the same as that provided by the Shaanxi Province Yearbook of Disaster Prevention, implying that the data from these different sources validated each other and that this catalog is reliable. According to the landslide classification of Cruden and Varnes (1996), which was

Table 1 Summary of the fields included in the catalogs. Category

Information on category

Site number Landslide type Location Nearest place

Unique ID for each landslide event Including slide and fall Latitude and longitude of the landslide event The nearest geographic location, including villages, cities and regions Year, month and day of the landslide event. Separate columns for the year, month and day.

Date

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obtained here. However, the time interval obtained here is our primary concern because the documented landslides are those that have affected the local the most. Thus, this catalog is very informative for landslide disaster prevention and mitigation. Therefore, it was appropriate to create this catalog and use it to investigate the temporal characteristics of landslides.

3.2.4. Exponential model Previous studies have shown that the probability distribution of time intervals for natural events follows an exponential distribution (Johnson et al., 1995). To quantitatively analyze the statistical characteristics of the time series of landslide events, we fit the CCF distribution of the time intervals between landslide events using the exponential function as follows:

3.2. Methods

CCF = αe−μT + βe−δT

3.2.1. Complementary cumulative frequency distribution Cumulative frequency (CF) is a widely used method for landslide frequency distribution (Pelletier et al., 1997; Dai et al., 2011; Guzzetti et al., 2002). The cumulative frequency distribution of landslides is the sum of a class and all classes below it in a frequency distribution of landslides. However, determining how often the cumulative frequency of landslides is above a particular value is useful. Therefore, we calculate the complementary cumulative frequency (CCF), which is the sum of the class and all classes above it in a frequency distribution, because we are interested in frequency values greater than or equal to a certain value. Therefore, the CCF is defined as follows:

where CCF is the complementary cumulative frequency of the time interval between landslide events. T is the time interval between landslide events (in days). α , β , μ and δ are constants. We model the CCF distribution of the time intervals to have a power-law distribution to estimate the parameters α , β , μ and δ based on the landslide catalogs. To determine the associated uncertainties, we calculated the 95% confidence bounds of the curve fitting. This relationship is important for assessing quantitative landslide risk and investigating mass-wasting erosion over landscapes. We can estimate the recurrence times of landslide events using the relationship proposed in this paper. This estimation is also important for engineering design, planning, and management on a regional scale.

CCF = 1 − CF

(1)

The CCF distribution of landslides determines the landslide hazard and risk. In the current study, we calculated the CCF distribution of the annual number of landslides and the interval of time between landslides. We then analyzed the annual number of landslides and the interval of time between landslides greater than or equal to a threshold value.

4. Results 4.1. Yearly temporal characteristics of landslide events 4.1.1. Yearly temporal distribution of landslide events Fig. 3 shows the annual number of landslides from 1996 to 2017 in the study area. The average annual numbers of slides and falls are approximately 17 and 10, respectively. The analysis of the annual number of landslides showed that there is large year-to-year variability. Furthermore, we used the Savitzky-Golay smoothing method in Origin 2016 software to smooth the data on the annual number of landslides. The results showed that the annual number of landslides exhibits a multimodal and approximately periodic distribution (Fig. 3). There are many landslide occurrences within certain continuous years. Therefore, we can divide the time series into active and nonactive periods by distinguishing the peak and trough of the wave shape. The active and nonactive periods alternated. These temporal variations in the annual number of landslides are commonly related to climatic factors. Moreover, we found a positive correlation between the annual numbers of slides and falls (Fig. 4). This finding suggested that many falls occurred in years with many slides because we focused on only nonseismically triggered landslides. Most of the slides and falls in this catalog were triggered by rainfall and occurred in the rainy season. Therefore, the annual number of slides is associated with the annual number of falls.

3.2.2. Concentration rate Many types of research have shown that the spatial and temporal distributions of landslides are clustered because the landslide distribution is strongly influenced by intensive rainfall events, earthquakes, and geomorphological and geological susceptibility factors (Lin and Wang, 2018; Qiu et al., 2019b). Previous studies have found that the annual average number of landslides is concentrated within certain months. Most landslides in a given year are concentrated in one or two months of the year. Most importantly, the one or two months with the most landslide occurrences change every year. To analyze this phenomenon, we defined the concept of concentration rate. The concentration rate in one month is defined as the ratio of the number of landslides during the month with the most landslides to the total number of landslides throughout the year. Similarly, the concentration rate in two months is defined as the ratio of the number of landslides in the two individual months with the most landslides to the total number of landslides throughout the year. The concentration rate can reveal the detailed structure of the temporal distribution of landslides and benefit the analysis of the time series of landslide occurrences.

4.1.2. Frequency distribution of the annual number of landslides We often consider the frequency value of an annual number of landslides greater than or equal to a certain value. Therefore, we calculated the CCF of the annual number of landslides using Eq. (2). We found that the CCF decreased with an increasing annual number of landslides (Fig. 5). Although there is limited theoretical basis for choosing a particular function, these relationships can be empirically described by a simple power-law function (Fig. 5). We obtained the empirical equations via linear least squares regressions. The p-values are < 0.001, and the coefficients of determination (R2) are high, suggesting that all the regressions are statistically significant. To consider the uncertainty associated with the parameters in the empirical equation, we determined the 95% confidence bounds of the curve fitting in linear coordinates (Fig. 5). This finding indicates that there exists a selfsimilar behavior between the annual number of landslides and its complementary cumulative frequency. These relationships can be used to estimate the probability of the annual number of landslides when the annual number of landslides is known. The probabilities that the annual number of falls and slides will exceed ten are approximately 28% and

3.2.3. Power law The magnitude-frequency distribution of earthquakes satisfies the Gutenberg-Richter law, i.e., a power-law relationship (Guzzetti et al., 2002). There is accumulating evidence that many frequency distributions of landslides also satisfy the power-law relationship (Guzzetti et al., 2002; Van Den Eeckhaut et al., 2007; Guthrie et al., 2008). To quantitatively determine the frequency of the annual number of landslides, here, we fit the CCF distribution of the annual number of landslides using the following power-law function:

CCF = aNL b

(3)

(2)

where NL is the annual number of landslides. a and b are constants. Furthermore, we calculate the 95% confidence bounds to determine the associated uncertainties in the curve fitting. Using Eq. (2), we calculate the probabilities of the annual number of landslides when the annual number of landslides is known, which may have important implications for landslide risk assessment in a given area. 4

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Fig. 3. Annual number of landslides and rainfall between 1996 and 2017. The bar chart shows the number of landslides. The dotted line shows the smoothed curve of the number of landslides based on the Savitzky-Golay smoothing method. The solid red and green lines show the active and non-active periods, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

48%, respectively. The probabilities that the annual number of falls and slides will exceed five are approximately 76% and 97%, respectively. Knowledge of landslide recurrences in time provides a basis for understanding landslide temporal behaviors and trends. 4.2. Monthly temporal characteristics of landslide events As shown in Fig. 6, approximately 69% of the total falls and 82% of total the slides occurred from July to October owing to the influence of continental monsoon activities. During this period, more precipitation falls and subsequently influences landslide occurrences and the corresponding distribution. Moreover, the monthly distribution of landslides shows a strong correlation with monthly rainfall (Fig. 6). Furthermore, the year can be divided into two parts. Most of the identified landslides occurred in the first part, from July to October. Few landslide events occurred in the other part, from November to June. Here, we focused on the frequency of the annual number of landslides in the months with the most landslide occurrences. Thus, we calculated the complementary cumulative frequency of the annual number of landslides from July to October and found that the relationships between the complementary cumulative frequency and the annual number of landslides from July to October can be described by a simple power-law function (Fig. 7). We fitted the data via the least-squares method in linear coordinates. The shaded area around the regression line represents the 95% confidence

Fig. 4. Relationship between annual numbers of slides and falls.

Fig. 5. The complementary cumulative frequency (CCF) distribution of the annual number of landslides. The solid line is the best fit obtained adopting a least-square fitting technique. Dashed lines indicate 95% confidence bounds. Data are shown in linear coordinates.

Fig. 6. Distributions of the monthly number of landslides and the monthly average rainfall in the considered period. The dashed lines show the cumulative number of landslides. 5

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concentration rate showed large year-to-year variability. The average concentration rates of falls in one and two months were 0.47 and 0.70, respectively. The average concentration rates of slides in one and two months were 0.48 and 0.72, respectively. These results suggest that the landslide distributions are clustered in time. Most of the landslides occurred in one or two months. This clustered temporal distribution pattern is associated with weather seasonality because most of the rainfall events occurred in one or two months. 4.4. Time series of landslide events and their time intervals 4.4.1. Time series of landslide events The number of landslides per day (DL) over the period from 1996 to 2017 is shown in Fig. 9. A large portion of the time series of DL is zero. The zero-value days account for 97.67% and 96.87% of the fall and slide time series, respectively. The nonzero values in the time series of DL exhibit highly unequal spacing. For the period of 1996–2017, the number of falls per day ranged from 0 to 5 day−1, with 187 different days having one or more falls. The number of slides per day ranged from 0 to 22 day−1, with 251 different days having one or more slides (Fig. 9). Rainfall plays a critical role in eliciting nonseismically triggered landslides. The time series of landslide events was influenced by intraday and antecedent rainfall. For example, we observed the landslide number, intraday rainfall and cumulative antecedent rainfall from July 6 to July 16, 2009, around Ankang city, Shaanxi Province (Fig. 10A). Seven landslides were triggered by continuous intraday and antecedent rainfall. Fig. 10B shows the continuous landslide occurrences and rainfall distribution from August 26 to September 5, 2003, in Shangnan city, Shaanxi Province. Clearly, the associated landslides were triggered by continuous and heavy rainfall. Moreover, an intensive and long-lasting rainfall event occurred from September 23 to October 3, 2005. This rainfall event triggered twenty-six landslides around Zhenan city, Shaanxi Province during this period. A lag effect exists between landslide events and the rainfall process because the antecedent rainfall reduces soil suction and increases pore-water pressure in soils (Fig. 10C).

Fig. 7. The complementary cumulative frequency (CCF) distribution of the annual number of landslides from July to October between 1996 and 2017. The solid line is the best fit obtained adopting a least-square fitting technique. Dashed lines indicate 95% confidence bounds. Data are shown in linear coordinates.

bounds of the empirical power-law equation. The results showed that the empirical regressions satisfy the statistical level of significance. This approach can be used to predict the frequency of the annual number of landslides in Shaanxi Province from July to October. 4.3. The concentration rate of the landslide monthly distribution Most of the landslides were concentrated in one or two months of each year due to the influence of rainfall activities on landslide triggers. For instance, all of the falls in 2000 and 2001 occurred in August and September, respectively. In 2005, 60% of the falls occurred in October. In 2011, approximately 71% of the falls occurred in September. In 2012, 75% of the falls occurred in July. Similarly, in 2005, 63% of the slides occurred in October. In 2010, 94% of the slides occurred in July. Approximately 69%, 71% and 75% of the slides occurred in September in 2011, 2012 and 2014, respectively. We calculated the concentration rates of the number of landslides in each year. As shown in Fig. 8, the

4.4.2. Time series of the time intervals between landslide events To research the time series of landslide events, here, we define a landslide event as all of the landslides occurring on a day with landslides, i.e., we take all the landslides in a day as a single landslide event. Fig. 8. Monthly concentration rates of landslides from 1996 to 2017. Red solid lines show the concentration rate of landslides in one month. Black solid lines show the concentration rate of landslides in two months. Dashed lines indicate the average concentration rate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 9. Number of landslides per day (DL) for the period from January 1, 1996, to December 31, 2017.

approximately 42 days. The time interval between slide events ranged from 1 day to 393 days, with an average time interval of approximately 32 days. The fall events with time intervals less than 10 days account for approximately 45% of the total falls. The slide events with time intervals less than 5 days account for approximately 44% of all the slides. As noted above, most of the identified landslides occurred from July to October, and we further divided the time series into two parts. This division is useful for accurately investigating the time interval between landslide events. The average time intervals of falls and slides from July to October are approximately 12 days and 8 days, respectively. Similarly, the average time intervals of falls and slides from November to June are approximately 34 days and 30 days, respectively (Fig. 12). The average time interval between landslide events from November to June is approximately three times as long as the interval from July to October. 4.5. Frequency distribution of the time intervals between landslide events 4.5.1. Frequency distribution of the time intervals between landslide events from July to October This temporal information on landslides can provide empirical thresholds that can be used to forecast landslide occurrences in the future. Owing to the impact of discontinuous rainfall activities, the temporal distribution of time intervals between landslide events in Shaanxi Province is extremely nonuniform. Short time intervals between landslide events are frequent, and long time intervals are rare. To precisely and quantitatively determine the frequency of the time intervals between landslide events, we calculated the complementary cumulative frequency of the time interval between landslide events from July to October (Fig. 12). Although there was limited theoretical basis for determining the specific functions for the complementary cumulative frequency and time interval between landslide events, the relationships were adequately fitted with exponential regressions according to a least-square fitting technique:

Fig. 10. The distributions of the number of landslides, intraday rainfall and cumulative antecedent rainfall. (A) From July 6 to July 16, 2009, around Ankang City, Shaanxi Province. (B) From August 26 to September 5, 2003, around Shangnan City, Shaanxi Province. (C) From September 23 to October 3, 2005, around Zhenan City, Shaanxi Province.

For falls: CCF = 0.44e−0.51T + 0.68e−0.06T

(4)

For slides: CCF = 0.81e−1.20T + 0.63e−0.08T

(5)

The minimum time interval between landslide events is one day. Fig. 11 shows the temporal sequence of landslide events from 1996 to 2017. The distribution of the time intervals showed features of intermittence, fluctuations, and clusters over time. The time interval between fall events ranged from 1 day to 390 days, with an average time interval of

where CCF is the complementary cumulative frequency of the time intervals between landslide events from July to October. T is the time interval between landslide events from July to October. To ascertain the uncertainty of the models, we determine the 95% confidence bounds of those regressions (Fig. 12). The results showed that coefficients of determination (R2) are very high and the root mean 7

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Fig. 11. Sequence of the time intervals between landslide events.

4.5.2. Frequency distribution of the time intervals between landslide events from November to June Similarly, we calculated the complementary cumulative frequency of the time interval between landslide events that occurred from November to June. The relationships between the complementary cumulative frequency and time interval between landslide events that occurred from November to June were adequately described by exponential functions (Fig. 13):

For falls: CCF = 0.79e−0.02T + 0.30e−0.47T

(6)

For slides: CCF = 0.80e−0.03T + 0.32e−0.38T

(7)

where CCF is the complementary cumulative frequency of the time intervals between landslide events from November to June. T is the

Fig. 12. The complementary cumulative frequency (CCF) distribution of the time intervals between landslide events from July to October. The solid blue and red lines show the best-fitting exponential regressions adopting a leastsquare fitting technique. Dashed lines indicate 95% confidence bounds. Box plots show the distribution of time interval between landslides from July to October. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

square error (RMSE) is very low. As illustrated in Fig. 12, CCF decreased with increasing time intervals between landslide events from July to October. The past landslide events are the key to predicting future landslides. Historical catalogs are the baseline for landslide temporal trends. These results indicate that we can adequately predict the probabilities of the time intervals for landslide events using Eqs. (4) and (5) in Shaanxi Province when the time intervals between landslide events are known. From the above two equations, we can infer that the probabilities of the time intervals being less than ten days are approximately 64% and 72% for all fall and slide events from July to October, respectively. The probabilities of time intervals less than five days are approximately 47% and 58% for all fall and slide events from July to October, respectively.

Fig. 13. The complementary cumulative frequency (CCF) distribution of the time intervals between landslide events from November to June. The solid blue and red lines show the best-fitting exponential regressions adopting a leastsquare fitting technique. Dashed lines indicate 95% confidence bounds. Box plots show the distribution of time interval between landslides from August to June. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 8

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high consistency, implying that we can utilize meteorological precipitation data to explore the relationship between precipitation and landsliding (Lin and Wang, 2018). Furthermore, we found that intraday rainfall, cumulative antecedent rainfall, and continuous and heavy rainfall play an important role in landslide occurrence. This topic was also discussed in many previous studies (Corominas and Moya 1999; Brooks et al. 2004; Cannon et al. 2008).

time interval between landslide events from November to June. According to the two equations, we can predict the probabilities of any time interval between landslide events from November to June using Eqs. (6) and (7) in Shaanxi Province. The numbers of time intervals less than ten days account for approximately 38% and 37% of the total number of time intervals for fall and slide events from July to October, respectively. The probabilities of time intervals less than twenty days account for approximately 48% and 52% of the total number of time intervals for fall and slide events from July to October, respectively. This result indicates that the CCF decreased with increasing time interval between landslide events. Similar to the cumulative frequencymagnitude of earthquakes, many short time intervals and few long time intervals were observed. The CCF of time intervals between landslide events was well fitted by an exponential function, indicating that the time series of landslide events exhibit clustering. Furthermore, this clustering of landslide events is associated with the clustering of precipitation events.

6. Conclusion This study developed a landslide catalog for Shaanxi Province using a combination of existing records of historical landslide events, the Yearbook of Disaster Prevention, local historical archives and chronicles. We found that the annual number of slides is significantly related to the annual number of falls. The distribution of the annual number of landslides exhibits periodicity. Active and nonactive periods appear in turn in the landslide distribution time series. The relationship between complementary cumulative frequency and annual number of landslides were empirically fitted by a simple power-law function. Most landslides occurred from July to October. Slide events were more common than fall events during the rainy season. We defined a concentration rate to measure the temporal distribution of landslides and found that the distribution of landslides is clustered in time. Most of the landslides occurred in one or two months of a year. The one-month concentration rate increased with increasing two-month concentration rate. The nonzero values in the time series of landslide events exhibited highly nonuniform spacing. The complementary cumulative frequency distribution of time intervals between landslide events can be adequately described by an exponent function. We expect that the findings of this paper will be helpful in landslide risk assessment.

5. Discussion In this work, we found that most of the landslides occurred in one or two months of a year. Nonzero values in the time series of landslide events were nonuniformly spaced. This result is consistent with the results of previous studies (Ibsen and Brunsden, 1996; Rossi et al., 2010; Tatard et al., 2010; Witt et al., 2010; Robbins and Petterson, 2015). Moreover, it is well known that the occurrence of earthquakes exhibits periodicity, and there are active and nonactive periods in the time series of earthquakes (Erdik, et al., 2004). Similarly, in the present work, we found that the annual number of landslides exhibited active and nonactive periods that alternated from 1996 to 2017. This pattern suggests that the time series of the annual number of landslides also exhibited an approximate periodic distribution, which is useful for predicting the activity of landslides in certain periods. Our results are similar to the findings of Lauknes et al. (2010), who found that the time series of landslides exhibit nearly periodic temporal spacing patterns, but our results differ from those of Piacentini et al. (2018) and Haque et al. (2016), who found that the number of landslides increased during the study period. Furthermore, we found that the CCF of the time interval between landslide events can be described by an exponential distribution under the 95% confidence bounds. Our results are similar to those of Johnson et al. (1995), Witt et al. (2010) and Guo et al. (2014) but differ from those reported by other authors who found that the probability distributions of the time intervals of volcanic eruptions, floods and landslides follow a Poisson, binomial or two-parameter Weibull distributions in many environmental time series (Coe et al., 2000; Önöz and Bayazit, 2001; Raetzo et al., 2002; Guzzetti et al., 2003; Bunde et al., 2005; Blender et al., 2008; Santhanam and Kantz, 2008; Witt et al., 2010). The temporally concentrated and clustered distributions of landslides during specific periods strongly coincided with the temporal distributions of earthquakes and asymmetrical distributions of climatic conditions, such as intensive rainfall and snowmelt events (Lang et al., 1999; Zhou et al., 2002; Carrara et al., 2003; Rossi et al., 2010; Tatard et al., 2010; Talling et al., 2014; Samia et al., 2017). The periodic distribution of landslides in time correlated with weather seasonality, earthquake events and anthropological activity (Garland and Olivier, 1993; Koukis et al., 2009; He et al., 2010; Rossi et al., 2010; Macciotta et al., 2017; Pan et al., 2019). The authors who found that the annual number of landslides increased in certain periods may have obtained incomplete inventories and collected more of the latest landslide information in the inventories. Moreover, we found that the monthly number of landslides shows a strong correlation with the monthly rainfall in Shaanxi Province. This finding is similar to those obtained by Huang and Li (2011), Lin and Wang (2018) and Piacentini et al. (2018), who found that the monthly distribution of landslides and rainfall show

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was funded by the International Science & Technology Cooperation Program of China, China (grant no. 2018YFE0100100), The Second Tibetan Plateau Scientific Expedition and Research (STEP) program, China (grant no. 2019QZKK0903), National Natural Science Foundation of China, China (grant no. 41771539), Strategic Priority Research Program of Chinese Academy of Sciences, China (grant no. XDA 20030301), International Partnership Program of Chinese Academy of Sciences, China (grant no. 131551KYSB20160002) and Key Laboratory of Degraded and Unused Land Consolidation Engineering of the Ministry of Natural Resources, China (grant no. SXDJ2019-07). References Aleotti, P., 2004. A warning system for rainfall-induced shallow failures. Eng. Geol. 73, 247–265. https://doi.org/10.1016/j.enggeo.2004.01.007. Bandara, S., Ohtsuka, S., 2017. Spatial distribution of landslides induced by the 2004 Mid-Niigata prefecture earthquake. Japan. Landslides 14 (6), 1877–1886. Bunde, A., Eichner, J.F., Kantelhardt, J.W., Havlin, S., 2005. Long-term memory: a natural mechanism for the clustering of extreme events and anomalous residual times in climate records. Phys. Rev. Lett. 94 (4), 048701. https://doi.org/10.1103/ PhysRevLett. 94.048701. Blender, R., Fraedrich, K., Sienz, F., 2008. Extreme event return times in long-term memory processes near 1/f. Nonlinear Process. Geophys. 15, 557–565. http://www. nonlin-processes-geophys.net/15/557/2008/. Brooks, S.M., Crozier, M.J., Glade, T.W., Anderson, M.G., 2004. Towards establishing climatic thresholds for slope instability: use of a physically based combined soil hydrology-slope stability model. Pure Appl. Geophys. 161 (4), 881–905. Cannon, S.H., Gartner, J.E., Wilson, R.C., Bowers, J.C., Laber, J.L., 2008. Storm rainfall conditions for floods and debris flows from recently burned areas in southwestern Colorado and southern California. Geomorphology 96 (3–4), 250–269. Carrara, A., Crosta, G., Frattini, P., 2003. Geomorphological and historical data in

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