Evaluating critical rainfall conditions for large-scale landslides by detecting event times from seismic records

One of the purposes of landslide research is to establish an early warning method for rainfall-induced landslides. The insufficient observations of the past, however, have inhibited the analysis of critical rainfall conditions. This dilemma may be resolved by extracting the times of landslide occurrences from the seismic signals recorded by adjacent seismic stations. In this study, the seismic records of the Broadband Array in Taiwan for Seismology were examined to identify the ground motion 15 triggered by large landslides occurring from 2005 to 2014. A total of 62 landslide-induced seismic signals were identified. The seismic signals provided the occurrence times of the landslides for assessment of the rainfall conditions, including rainfall intensity (I), duration (D), and effective rainfall (Rt). Comparison of three common rainfall threshold models (I–D, I–Rt, and Rt–D) revealed duration and effective rainfall to be the crucial factors in developing a forecast warning model. In addition, a critical height of water model combining physical and statistical approaches, (I-1.5)·D = 430.2, was established through 20 analysis of rainfall information from the 62 landslides that occurred. The critical height of water model was applied to Typhoon Soudelor of 2015 and successfully issued a large landslide warning for southern Taiwan.


Reply to the comments of editor
We have now received two reviews and two very detailed answers by the authors, along with some modified sections of the manuscript + some possible Annexes. All these support the improvement of the manuscript. We encourage the authors to submit their final revised version of the manuscript assuming also: -a careful technical review of the grammar (some mix of passive/active voices are used -please homogeneize) and figures (some typos errors in some of them) for instantce Guezzeti instead of Guzzetti on figure 6, and so on) -a more in depth discussion on the generosity of the approach used for establishing the EW thresholds in other cases ... R: The authors deeply appreciate the editor's reviewing and providing valuable suggestions to improve the manuscript. The authors have improved the English writing of the manuscript through a language editing service to make sure that the article is free of grammatical, spelling, and other common errors.
The authors have made a more in-depth discussion on the application of rainfall threshold to Typhoon Soudelor of 2015. All thresholds proposed in the study have been tested in the case study. The illustration has been made in the section 5.1 as follows: "To verify the usability of the rainfall thresholds proposed in this study, Typhoon Soudelor of 2015 was chosen to demonstrate the early warning performance.
Typhoon Soudelor was one of the most powerful storms on record. It generated 1400 mm of rainfall in northeastern Taiwan and almost 1000 mm of rainfall in the southern mountainous area of Taiwan (Wei, 2017;Su et al., 2016). After the seismic signal analytical procedure, the occurrence time, 2015/8/8 18:59:50 (UTC), of a large landslide (named the Putanpunas Landslide) located in southern Taiwan was obtained (Fig. 7). The seismic signal generated by the Putanpunas Landslide was also detected by Chao et al. (2017). The seismic signals generated by this large landslide could be identified from six BATS stations, and the distance error was less than 6 km. The rainfall records of rain gauge station C1V190, which was situated in the same watershed and 14.6 km away from the large landslide, were collected for rainfall analysis. Typhoon Soudelor made landfall in Taiwan on August 7, 2015, and dropped a cumulated rainfall of 546 mm and had a maximum rainfall intensity of 39 mm/h on August 8 at rain gauge station C1V190 (Fig. 8).
The rainfall event began at 22:00 August 7 and last for 26 hours, and the Putanpunas Landslide initiated at the 22nd hour. This landslide occurred when the rainfall intensity was on the decline.
Regarding landslide early warning using rainfall thresholds, once the rainfall conditions at a given rainfall station exceed the rainfall thresholds for triggering landslides, the slopes located within the region of the rainfall station will have high potential for failure. Based on the statistically-based I-D threshold for small landslides, a small-landslide warning would have been issued at the sixth hour of the rainfall event (Fig. 8). The long interval of sixteen hours between the warning and the occurrence time of the Putanpunas Landslide could have reduced the reliability of the warning or even caused the warning to be considered a false alarm.
Therefore, it is essential to establish different thresholds for landslides of different scales. Using the I-Rt threshold (i.e., Rt·I= 5,640), a large-landslide warning would have been issued at the ninth hour of the rainfall event (i.e., thirteen hours before the Putanpunas Landslide occurred). According to the statistically-based I-D threshold for large landslides, a landslide warning would have been issued at the same hour as the I-Rt threshold. In addition, a warning based on the Rt-D threshold

Reply to the comments of reviewer #1
Kuo et al., present a landslide catalogue in Taiwan, obtained by remote sensing, from which they extract 62 large landslides that can be accurately timed thanks to seismic detection, and compared to local rainfall gaging data. Then they assess which type of rainfall threshold could be derived for this dataset, including a threshold guided by physical considerations, and compare it to a dataset of smaller landslides in Taiwan. The paper ends with a rather unconvincing or unclear discussion on potential variabiliy of the thresholds and on issues sith seismic detection.
Overall, the authors present an interesting, novel dataset (although relatively modest) and do a series of classic (rainfall threshold) and less classic (physically based threshold) analysis that can be worth publishing, but the discussion and some of the analysis need to be improved before that. R: The authors very much appreciate the reviewer's valuable time, comments and suggestions.
(1) Major comment 1. Timing is an issue but rainfall estimation as well. Notably because rain gage may be far from the landslides and not experiencing similar rainfall especially due to orographic effects. The author explain they only associate landslide with rainfall measured within 100km 2 . I think this is a good start but in the analysis it would be good to indicate (by a color coding?) the horizontal distance from the landslide, as well as to discuss difference in elevation between station and landslide median elevation for example. This would allow the authors to discuss uncertainty and the degree of reliability of rainfall estimates for the landslides. R: The authors appreciate the reviewer's constructive suggestion. The spatial information (distance and elevation) of each used rain gauge station has been added to supplementary materials as Table S2. The effect of rain gauge distribution over the accuracy of rainfall has been assessed using gauge observation in a 35 km × 50 km region of south Taiwan (Fig. S2). The amounts of daily rainfall during 2009 Typhoon Morakot (8/6-8/11) recorded at 19 rain gauge stations were selected to validate the accuracy of rainfall. At first, the amounts of daily rainfall were interpolated to 01V040 station using IDW methods. The errors between measurements and interpolated data were smaller than 15 %. It indicates IDW method can be used to interpolate rainfall to a selected location in our study area.
Secondly, the amounts of daily rainfall at the central point of the 35 km × 50 km region were estimated. The errors of daily rainfall between the central point and the nearest rain gauge station (01V040) were smaller than 10 % (0.5%-10% at different date).
Besides, the correlation coefficients would keep at 90% as a distance between the central point and rain gauge stations less than 20 km, and even keep at 98% as a distance less than 10 km (Fig. S3). Therefore, in the study, an upper limit of basin area smaller than 100 km 2 (10 km × 10 km was adopted to avoid a significant decrease of the accuracy of rainfall. The influence of topography on rainfall variability has been analyzed in the same 35 km × 50 km region of south Taiwan. The highest station elevation is 1792 m a.s.l. at C1V270, and the lowest station elevation is 105 m a.s.l. at C10830. The standard deviation of station elevation is 561 m. The values of standard deviation of daily rainfall at the 19 stations were calculated, and less than 13% except a high standard deviation, 45%, on August 6 (average daily rainfall less than 2 mm). The results demonstrated that high and even extreme rainfall are less influenced by elevation, while low and medium rainfall events are significantly influenced by elevation variation, with most of the rainfall appearing on high elevations. Similar results have also been reported by some previous studies (Sanchez-Moreno et al., 2014;Ge et al., 2017). Because the study only considered the rainfall events with total cumulated rainfall greater than 500 m, the elevation effect was ignored as selecting rain station. The above illustration has been attached to the supplementary material S3. The authors appreciate the reviewer's suggestions and agree that the comparison of physically-based and statistically-based thresholds is needed. The study focused on rainfall conditions for triggering landslides in a wide (national scale) study area, a purely physical model may be not suitable. We would like to call it a mixed physicallyand statistically-based model. The rainfall threshold using a mixed physically-and statistically-based model in the study will be compare with others using physicallybased models. The relative discussion has been added to the text as below.
"In general, physically-based models are easy to understand and have high predictive capabilities Wieczorek, 1995: Salciarini andTamagni, 2013;Papa et al., 2013;Alvioli et al., 2014). However, they depend on the spatial distribution of various geotechnical data (e.g., cohesion, friction coefficient, and permeability coefficient), which are very difficult to obtain. Statistically-based methods can include conditioning factors that influence slope stability, which are unsuitable for physically-based models. Statistically-based models rely on good landslide inventories and rainfall information. In this study, the threshold for a large landslide was estimated based on a mixture of physically-and statisticallybased methods. Unlike other physically-based I-D thresholds, which are commonly constructed based on artificial rainfall information for shallow landslides (Salciarini et al., 2012;Chen et al., 2013c;Napolitano et al., 2016) (Table S3), the threshold proposed in this study seemed to be higher and more suitable for large landslides (Fig. 6d)." "To verify the usability of the rainfall thresholds proposed in this study, Typhoon Soudelor of 2015 was chosen to demonstrate the early warning performance.
Typhoon Soudelor was one of the most powerful storms on record. It generated 1400 mm of rainfall in northeastern Taiwan and almost 1000 mm of rainfall in the southern mountainous area of Taiwan (Wei, 2017;Su et al., 2016). After the seismic signal analytical procedure, the occurrence time, 2015/8/8 18:59:50 (UTC), of a large landslide (named the Putanpunas Landslide) located in southern Taiwan was obtained (Fig. 7). The seismic signal generated by the Putanpunas Landslide was also detected by Chao et al. (2017). The seismic signals generated by this large landslide could be identified from six BATS stations, and the distance error was less than 6 km. The rainfall records of rain gauge station C1V190, which was situated in the same watershed and 14.6 km away from the large landslide, were collected for rainfall analysis. Typhoon Soudelor made landfall in Taiwan on August 7, 2015, and dropped a cumulated rainfall of 546 mm and had a maximum rainfall intensity of 39 mm/h on August 8 at rain gauge station C1V190 (Fig. 8).
The rainfall event began at 22:00 August 7 and last for 26 hours, and the Putanpunas Landslide initiated at the 22nd hour. This landslide occurred when the rainfall intensity was on the decline.
Regarding landslide early warning using rainfall thresholds, once the rainfall conditions at a given rainfall station exceed the rainfall thresholds for triggering landslides, the slopes located within the region of the rainfall station will have high potential for failure. Based on the statistically-based I-D threshold for small landslides, a small-landslide warning would have been issued at the sixth hour of the rainfall event (Fig. 8). The long interval of sixteen hours between the warning and the occurrence time of the Putanpunas Landslide could have reduced the reliability of the warning or even caused the warning to be considered a false alarm. Therefore, it is essential to establish different thresholds for landslides of different scales. Using the Rt-I threshold (i.e., Rt·I= 5,640), a large-landslide warning would have been issued at the ninth hour of the rainfall event (i.e., thirteen hours before the Putanpunas Landslide occurred). According to the statistically-based I-D threshold for large landslides, a landslide warning would have been issued at the same hour as the Rt-I threshold. In addition, a warning based on the D-Rt threshold (i.e., D·Rt= 12,773) would have been issued three hours after the occurrence time of the Putanpunas Landslide. According to the rainfall records and the critical height of water model (i.e. (I-1.5)·D=430.2), a landslide warning would have been issued at 16:00 on August 8, three hours before the occurrence time of the Putanpunas Landslide. Compared to the statistically-based I-D threshold, the Rt-I threshold, and the D-Rt threshold, the critical height of water model had a better early-warning performance for the 2015 Putanpunas Landslide."    I0)×D=Qc, was adopted to fixed the lower boundary of rainfall data in the I-D plot. The value of I0 was estimated using the same statistically-based method with I-Rt threshold. The value of 1.5 was obtained as the exceeding probability of 5%. We would like to call it a mixed physically-and statistically-based model. The mixed model could recover the limitation while we just used a purely physically-based model or a purely statistically-based model. The comparison of the critical height of water model with other studies has been added in Figure 6, and table S3. The modified illustration has been added to the test as below: "In this study, the threshold for a large landslide was estimated based on a mixture of physically-and statistically-based methods. Unlike other physicallybased I-D thresholds, which are commonly constructed based on artificial rainfall information for shallow landslides (Salciarini et al., 2012;Chen et al., 2013c;Napolitano et al., 2016) (Table S3), the threshold proposed in this study seemed to be higher and more suitable for large landslides (Fig. 6d)." 4. Last, I strongly suggest the authors to define variable names for antecedent rainfall (e.g. Ra), cumulated rainfall (e.g. Rc) to later compare with Rt (Rt = Rc + Ra) and to be consistent in text and figure when they talk about rainfall amount. R: Thanks for the suggestion. The variable names have been modified according to the suggestions.
(2) Line by Line comments: 1. P2 L 5: LSL / SSL : this is heavy and makes the draft harder to read. Why not simply use small and large landslide and indicating the boundary is at 0.1km 2 ? R: Thanks for the suggestion. The origin term, large-scale landslide and small-scale landslide, have both replaced with "large landslide" and "small landslide", respectively.
2. P2 L21: State in the text how was estimated the occurrence time. Based on peak rainfall correct? In Fig 1 Caption you say that in general peak rainfall intensity is used. This may go int the main text, with one or two references. Indeed, simple groundwater modelling (e.g. Wilson and Wieczorek, 1995) could estimate soil moisture based on the rainfall data and find a maximal pore pressure after the peak rainfall. Other simple modelling approach or assumption may give different estimation times. R: Thanks for the suggestions. The authors agree that more and more useful approaches have been developed to get the exact time information of landslide initiation. However, the approaches all depended on in-situ monitoring or other assumptions. So far, the most common and convenient way to assess a factor of rainfall intensity is still based on the peak rainfall intensity. The statement on peak rainfall intensity has been added to text with some references (i.g. Chen et al., 2005;Wei et al., 2006;Staley et al., 2013;Yu et al., 2013;Xue et al., 2016). The study uses the time interval between the timing with peak rainfall intensity and exact landslide timing to explain the misjudgment results of rainfall analysis (Chen et al., 2005). The reference have been added to text as below: "…In general, if the exact occurrence time of a landslide cannot be investigated, the time point with the maximum hourly rainfall will be conjectured as the occurrence time of the landslide (Chen et al., 2005;Wei et al., 2006;Staley et al., 2013;Yu et al., 2013;Xue et al., 2016).…."
3. P2 L34: Fractural geological conditions >> Fratcured rock mass R: Thanks for suggestion. The sentence has been revised based on the suggestion as below.
"…. Fractured rock mass coupled with a warm and humid climate, and an average of 3 to 5 typhoon events per year, contribute to the high frequency of slope failures in mountainous areas in Taiwan (Wang and Ho, 2002;Shieh, 2000;Dadson et al., 2004;Chang and Chiang, 2009;Chen, 2011)..…" 4. P2 L35: slope disasters >> I would suggest slope failures , more general (here and at other place in the text) R: Thanks for suggestion. All sentences contained the term "slope disaster" have been replaced with "slope failure" based on the suggestion. For example: "…The rainfall intensity, however, could not be used effectively to distinguish these two kinds of slope failures.…." 5. P3 L21: By a rainstorm (which one?) or by the Morakot typhoon ? Please clarify. R: Here refers to landslides caused by heavy rain events, not only by a specific event, we will modify the statement to avoid confuse. The modified text is as follows: "…Landslides induced specifically by rainstorm events were distinguished by overlaying the pre-and post-event image mosaics.…." 6. P3 L25: end of the sentence unclear. Main factor to separate SSL from LSL or to relate to rainfall triggering? If so how? R: In the study, the landslide types were divided into large landslide and small landslide based on the size of landslide-disturbed area. The rainfall factors of each landslide were assessed after classifying. The main purpose in the study is to find the difference of rainfall thresholds between large and small landslides, but not to classify these two types of landslides by rainfall factor or rainfall pattern. The relative sentence will be revised to avoid confuse. The modified text is as follows: "…Finally, large and small landslides were distinguished and classified according to the criterion of an affected area of 0.1 km 2 . In this study, the types and mechanisms of individual landslides were not investigated, but landslide area was used as the main factor for investigating the different rainfall conditions that trigger large and small landslides." 7. P3 L 30: Ok the triangular signature is typical, but could you cite and discuss what are other typical properties? I know there are quite some papers discussing how to detect and classify landslides based on various properties of the spectrogram or of the waveform. R: The authors thank the reviewer's suggestions. More deeply description on the features of landslide-induced seismic signals will be added to the text as bellows: The modified text is as follows: "…The seismic wave generated by a landslide can be attributed to the shear force and loading on the ground surface as the mass moves downslope. Many studies have shown that the source mechanism of a landslide is highly complicated, and that its seismic waves mainly consist of surface waves and shear waves, making it difficult to distinguish P and S waves from station records Suwa et al., 2010;Dammeier et al., 2011;Feng, 2011;Hibert et al., 2014). The onset of a landslide seismic signal is generally abrupt. Then the seismic amplitude increases gradually above the ambient noise level to peak ground motion, exhibiting a cigar-shaped envelope. After the peak amplitude, most of the landslide-generated seismic signals have relatively long decay times, on average about 70% of the total signal duration (Norris, 1994;La Rocca et al., 2004;Suriñach et al., 2005;Deparis et al., 2008;Schneider et al., 2010;Dammeier et al., 2011;Allstadt, 2013). In the frequency domain, landslide-induced seismic energy is mainly distributed below 10 Hz, with a triangular signature in a spectrogram, due to an increase over time in high-frequency constituents (Suriñach et al., 2005;Dammeier et al., 2011). The triangular signature in the spectrogram is the distinctive property that readily distinguishes landslideinduced signals from those of earthquakes and other ambient noise." Reference: The modified text is as follows: "…The distribution of precipitation during typhoon events is usually closely related to the typhoon track and the position of the windward slope, also as known as the orographic effect. In addition, the density and distribution of rainfall stations in mountainous areas directly affect the results of rainfall threshold analysis. If the landslide location and the selected rainfall station are located in different watersheds, the rainfall information is unlikely to represent the rainfall conditions for the landslide. In some cases, however, the diameter of the typhoon were so large that the orographic effects could be ignored (Chen and Chen, 2003

P5 L 14: Say if this is your definition (we define the beginning of a rain event)
or a general one (then cite other studies.) R: Thanks for comments. The sentence has been revised as follows: "…In rainfall analysis, the beginning of a rain event is defined as the time point when hourly rainfall exceeds 4 mm, and the rain event ends when the rainfall intensity remains below 4 mm/h for 6 consecutive hours. The critical rainfall condition for a landslide was calculated from the beginning of a rain event to the occurrence time of the landslide (Jan and Lee, 2004;Lee, 2006) 13. P5 L18-20: I understand it is hard to choose objectively which time should be considered for antecedent rainfall, but an arbitrary threshold without temporal weighting seems disingenuous... It is fair to use the official definition but what about testing a coupd other antecedent rainfall conditions: for example, the cumulated rain over 3 or 5 days. Or a weighted sum over the 10 preceding days (with weight decreaseing with time before the event). R: Thanks for your suggestion. In this study we used a temporal weighting coefficient of 0.7 with weight decreasing with days before the event (Jan and Lee, 2004). The formula can be written as: We have attached this in a later version. The modified text is as follows: "…In addition to the three factors mentioned above, the daily rainfall for the seven days preceding the rainstorm was considered as antecedent rainfall (Ra).
The antecedent rainfall (Ra) was calculated with a temporal weighting coefficient of 0.7, with the weight decreasing with days before the event. The formula was is the daily rainfall of the i th day before the rainfall event…" and property. In some cases, in-situ steel cables or closed-circuit television recorded the time information. This information was applied to the rainfall data analysis and then used to compare the rainfall conditions of the large landslides." 15. P6: Subsection 2.4: missing "l", >> water model ? R: Thanks for careful reviewing. The mistake has been revised in the text.
16. P6 EQ 1 and 2: ok but the assumption C' = 0 maybe quite a big one , especially for large bedrock landslides... Need to be discussed at some point, because Qc would be larger with none zero C. R: We thanks reviewer's recommendation. Well development of detachment plane (e.g., sliding surface between sedimentary layers, connected joints, weathered foliation, etc.) have been widely considered as the geological conditions to occur a large landslide (Agliardi et al., 2001;Tsou et al., 2011). Therefore, in the study, the C' of the detachment plane is simply assumed as the value of zero to behave the critical situation of slope stability. The illustration of C' has been modified to the text.
The modified text is as follows: "where Z is the vertical depth of the sliding surface, is the unit weight of the slope material, and is the slope angle. Good development of a detachment plane (e.g., sliding surface between sedimentary layers, connected joints, and weathered foliation) has been widely considered as the geological condition under which a large landslide occurs (Agliardi et al., 2001;Tsou et al., 2011). Therefore, in this study, the c' of the detachment plane is simply assumed to be zero to represent the critical situation of slope stability." 17. P6 EQ 4: Qc is actually the height of saturated regolith above the failure plane, in mm. Maybe clearer than calling it a critical volume. Note that in EQ 3 it is a critical height. But in EQ 4 it is simply a height assuming I0 is correctly estimated.

Reference
Another key issue is that this equation does not account for the antecedent rainfall. As I and D are for the triggering storm only, correct? Finally, I do not see why the authors assume a linear drainage. Most hydrological simple model of soil drainage (backed up by theory and observations) show a non linear drainage rate, where drainage increase with the amount of water in the soil (e.g., Wilson and wieczorek, 1995). I think the authors should discuss this choice here or in discussion. This model is very easy to implement and use to obtain soil water level, only requiring the hourly estimate of rainfall and an assumed drainage parameter. I think it may be an interesting addition to the paper to really make the authors model physical. I note that a number of recent attempt to model physically landslide threshold (cf major comments) should be mentioned and discussed here and/or in discussion these models and how they compare to the author proposition. R: Thanks for the valuable suggestions. The original naming of Qc in the manuscript is followed the Keefer (1987). We have revised the naming of Qc to critical water height.
Practically, antecedent rainfall is not considered in the empirical/statistically-based I-D method.
18. P7 L5: "their slope angles". Do you mean the mean slope within the landslide body? R: The slope angles mentioned in the study indicate the mean slope gradient before landslides occurred. The values of slope gradient were utilized to calculate Qc, therefore they should not be affected by landsliding. The slope angles were estimated with a 40 m digital elevation model (DEM) which was created before 2004. The illustration on slope angles will be modified as below.
"…. Most of these large landslides had areas of 0.12 to 0.15 km 2 , and their slope angles before the landslides occurred were concentrated between 30° and 40° ( Anything else? One sentence for recalling the reader of the criteria used would be helpful R: After obtaining the signal at the time of the landslide events, we use the locating method proposed by Chen et al. (2013) to locate the vibration source. Once a landslide is close to a locating point of seismic records and the slope aspect of the landslide is consistent with the direction of signal trajectory, the landslide can be considered as the source of the seismic signals.
22. P8 L25: Interesting, but size is not the only difference with these other thresholds. The fact you focused on large landslides, requiring higher total rainfall, and thus higher I-D lines is likely contributing. However, how much of the difference could be due to seismic dating? To the regional characteristics of the landslide (as some threshold are global, other Taiwanese or Japanese). I think these should be mentioned here or in discussion, because your threshold for SSL is also much larger than most other threshold, and these SSL are more similar in size to past study. R: Thanks for suggestions. The study aims to use a seismicity method to get landslide timing for constructing rainfall thresholds, and to discuss which threshold is more suitable to give different warning for small and large landslides. Clearer illustration of the purpose of the study has been added to the introduction section as below: "This study attempts to determine the occurrence times of landslides by identifying landslide-generated seismic signals to construct rainfall thresholds, and to clarify which thresholds are more suitable for triggering different warnings for small and large landslides…."

P9 L 1-2: it was determined that Rt-D analysis could be used effectively to distinguish SSLs from LSLs. I think it is very interesting to see in Fig 5B that
the landslide size groups shift from small for relatively short duration and low rainfall amount to large landslides for long and very large cumulative rainfall. R: Thanks for comments. We have added the illustration to the modified manuscript as below: "The landslide size groups shifted from small landslides for relatively short duration and low effective rainfall to large landslides for long duration and very large effective rainfall." In any case this plot is also quite interesting, as it matches well the theoretical expectations (Van asch 1999, Iverson 2000) stating that very large landslides will require high cumulated rainfall (unlikely to accumulate over short timescales) while small landslides may be caused by transient pulse of water accumulation in the shallow regolith relating to very high intensity, but that do not need to cumulate large amount of water. R: We thanks for comments. The statement has been revised as below: "…Combining the results of the three kinds of dual-factor rainfall threshold analyses revealed that the critical rainfall conditions for small landslides included high average rainfall intensity but relatively low effective rainfall, while those for large landslides included long rainfall duration and high effective cumulated rainfall. These results corresponded well with the former theoretic expectation (Van Asch et al., 1999;Iverson, 2000)." The modified text is as follows: "…However, prolonged rainfall also plays an important role in slow saturation, which in turn influences the groundwater level and soil moisture, and causes large landslides. These facts have been recognized in many studies around the world (Wieczorek and Glade, 2005;Van Asch et al., 1999;Iverson, 2000), but they have been analysed in only a few locations (e.g., a mountainous debris torrent, a shallow landslide event, and an individual rainfall event)…." The modified text is as follows:

P9
"The critical height of water, , on a sliding surface for each large landslide was estimated based on its slope gradient, depth (estimated by the equation Z = 26.14A 0.4 ; Z: depth in m; A: disturbed area in m 2 ), and the geological material parameters of the study area (Table 1) Table S2). To determine the limits of large landslide detection distance as a function of event volume, we selected the farthest seismic station at which each event was detectable. An event was deemed detectable when we had selected the station for the distancedependency analysis. The remaining results are shown on a plot of distance versus disturbed area (Fig. 9), where we can observe an upper detection limit described by equation 5. If, for a given event, a station plots in the lower right area below the dashed line (equation (5)), the seismic signal should be detectable. The detection limit also depends on the station signal quality; if the noise level is high, the signal may be obscured, even though a station farther away with a lower noise level will still record it clearly. Similar studies had been reported by Dammeier et al. (2011) and Chen et al. (2013).

P11 Eq 5: to discuss validity and limits of EQ 5 it should be made clearer how
(empirically?) and with which dataset/environment this relationship was obtained. R: The authors appreciate reviewer's recommendation. In the study, the lower boundary of detection was determined empirically based on two lowest values of the farthest distance of detection (i.g. 31.0 km and 37.6 km) having the disturbed areas of 1.6× 10 5 and 1.2×10 5 m 2 . Dammeier et al. (2011) used a similar way to get their equation of the lower boundary of detection. The modification has been added to text as follows: "…The boundary of detection was determined empirically based on the two lowest values of the farthest distance of detection (i.e., 31.0 km and 37.6 km) having disturbed areas of 1.6×10 5 and 1.2×10 5 m 2 . For a given large landslide, if a station is located below the upper detection limit, the seismic signal should be detectable.
However, not all the stations located in detectable regions recorded clear large landslide-induced seismic signals.…"

Fig 3: closest station is MASB (in the caption) or SGSB (in the map) ? It means
90% of the landslide and seismic signal R: We deeply thanks for careful inspection. The closest station should be SGSB. The mistake has been revised in Figure 3 of the later version of manuscript.

Fig 5: The last panel is not very clear: Cumulated rainfall is the total rainfall
in the triggering storm. Antecedent rainfall has no reason to be compared directly with landslide occurrence, but only when summed with the cumulated rainfall. So why not show Rt the total effective rainfall together with Rc the cumulative rainfall (Given that Rt>= Rc it should be easy to visualize). R: Thanks for the constructive suggestion. The last panel in Figure 5 has been revised to display Rt and Rc. The revised Figure 5 is as below:   What is driving the (small) difference in threshold curve is only 1 or 2 points out of each subset (that seems to be15-25 points). These low points shift the threshold while the bulk of each population do not seem different in any way. I am convinced this can only be due to chance and not to a shift of the whole population. I am even surprised that the curves are so low because if they are the 5% exceedance probability ~1 point should be left out in subset of ~20...

R:
We appreciate the valuable comments, and decided to remove this section. Meanwhile, we added a section to illustrate the validation of the rainfall thresholds mentioned in the study and other previous studies. To determine the limits of large landslide detection distance as a function of event volume, we selected the farthest seismic station at which each event was detectable. An event was deemed detectable when we had selected the station for the distancedependency analysis. The remaining results are shown on a plot of distance versus disturbed area (Fig. 9), where we can observe an upper detection limit described by equation 5. If, for a given event, a station plots in the lower right area below the dashed line (equation (5)), the seismic signal should be detectable. The detection limit also depends on the station signal quality; if the noise level is high, the signal may be obscured, even though a station farther away with a lower noise level will still record it clearly. In total, 62 data points in Fig. 9. Each data point represents the distance between landslide location and the farthest detectable station as well as landslide-disturbed area.
In the order words, it indicate that landslide signals can be detectable as the distance between landslide and seismic station shorter than the value of data. Therefore, to determine a lower boundary of these data can demarcate an effectively detectable region. The illustration of section 5.2 has been modified as follows: Seismology is around 30 km. A higher density of seismic stations would improve the detection function. In addition, to determine the limitation of large landslide detection distance as a function of large landslide-disturbed area, the most distant seismic station where large landslide signals were visible was selected. Some previous studies have applied similar approaches to probe the detection limit (Dammeier et al., 2011;Chen et al., 2013). The relationship between the maximum distance of detection and the large landslide-disturbed area shows a limitation of the detection distance due to the large landslide's magnitude (Fig. 9). In Figure 9, each data point represents the distance between a landslide location and the most distant seismic station detecting it, as well as the landslide-disturbed area. In other words, when the distance between a seismic station and a landslide that has the same given landslide-disturbed area as the data is shorter than the value of the data, seismic signals induced by the landslide can be interpreted from the records of the seismic station. Therefore, a lower boundary of these data can be determined to demarcate an effective detectable region. As a large landslide's area increases, the maximum distance between the large landslide location and seismic detection increases. A detection limit can be described by The boundary of detection was determined empirically based on the two lowest values of the farthest distance of detection (i.e., 31.0 km and 37.6 km) having disturbed areas of 1.6×10 5 and 1.2×10 5 m 2 . For a given large landslide, if a station is located below the upper detection limit, the seismic signal should be detectable.
However, not all the stations located in detectable regions recorded clear large landslide-induced seismic signals. One of the possible reasons is that the environmental background noise affected the signal to noise ratio of the seismic records during heavy rainfall events. Therefore, the detection limit may also depend on the signal quality at each station." 1) Some confusing statements (e.g. landslide number, topic event, study period, etc.)

References not used in
will be modified in the revised manuscript.
2) The authors will provide and modify the description of data sources, quality, and accuracy (including rainfall information, satellite image, and seismic records).
3) More in-deep discussion on results will be added in the modified version.
4) The suggested modification of methods and figures will be done in the manuscript.
Specific comments: 1. P2 L21: the event of 2009 is the only one mentioned, for the moment we can think that the research only focus on this event. R: The authors appreciate the reminding. We agree that the current manuscript may confuse readers due to many examples belonging to Typhoon Morakot. In the study, totally nineteen rainstorm events (seventeen typhoon-induced events and two heavy rainfall events) in the period of 2005-2014 were selected to examine the seismic records, but not only one event. The modified manuscript will clearly descript the targets in the section of introduction and study materials. The list of selected typhoons and heavy rainfall events will be added to the modified version (Table S1).
In the original manuscript, Typhoon Morakot was mentioned many times because it was one of the most tragic event in Taiwan in the past 20 years (more than 20,000 landslides, and more than four hundred large landslides with the disturbed area larger than 0.1 km 2 ), and therefore many good examples can be shown. In the modified version, the examples of other events have been provided in the supplementary material. The modified text is as follows: "…In this study, a total of nineteen rainstorm events (seventeen typhoon-induced events and two heavy rainfall events) in the years 2005-2014 were selected to examine the seismic records (Table S1) Table S2. Landslide mapping was conducted for nineteen rainstorm events (seventeen typhoon-induced events and two heavy rainfall events).

P3 L23: Why 0.1km² Is it the limit of the automatic detection based on SPOT
images? How many landslides were detected? R: Based on the definition and characteristic of deep-seated gravitational slope deformation (DSGSD) and description of large-scale landslides (Lin et al., 2013a;Lin et al., 2013b), a large-scale landslide should have three characteristics, including 1) a depth larger than 10 m, 2) a volume greater than 1000,000 m 3 , and 3) a speedy movement velocity. In practice, it is difficult to get these three characteristics without in-situ investigation and geodetic survey. Therefore, we chose the disturbed area of 100,000 m 2 (0.1 km 2 , volume/depth) as the indicator to sort large-scale landslides from other types of slope failure. Landslide interpretation with satellite imagery is the fastest way to classify large-scale landslides. Actually, more than three hundred seismic signals The modified text is as follows: "…Landslides induced specifically by rainstorm events were distinguished by overlaying the pre-and post-event image mosaics. Based on the definition and description of deep-seated gravitational slope deformation (DSGSD) and large landslides (Lin et al., 2013a;Lin et al., 2013b), a large landslide should possess three characteristics: 1) a depth larger than 10 m, 2) a volume greater than 1,000,000 m 3 , and 3) a high velocity. In practice, it is difficult to confirm these three characteristics without in-situ investigation and geodetic survey. Therefore, a disturbed area of 100,000 m 2 was determined as an accommodating indicator to sort large landslides from small landslides. Finally, large and small landslides were distinguished and classified according to the criterion of an affected area of 0.1 km 2 . In this study, the types and mechanisms of individual landslides were not investigated, but landslide area was used as the main factor for investigating the different rainfall conditions that trigger large and small landslides." 4. P3 L26: How we consider the progressive instability and the signal before the main failure? R: The authors agree that investigation of progressive instability is quite important. We believe that even slight displacement of materials on slope can stir energy transfer and induce seismic signals. However, the seismic signals generated by the processes of progressive deformation/displacement of material on slope do not contain enough energy to be recorded by remote seismic stations. Therefore, we did not try to monitor creeping processes by seismicity-approaches. "…To reduce the uncertainty caused by manual identification, events with obvious triangular signatures in the spectrograms (e.g. Fig. S1) were used to examine rainfall statistics in this study." The in-deep description of the characteristics of landslide-induced seismic signals has been added to text as follows: "…The seismic wave generated by a landslide can be attributed to the shear force and loading on the ground surface as the mass moves downslope. Many studies have shown that the source mechanism of a landslide is highly complicated, and that its seismic waves mainly consist of surface waves and shear waves, making it difficult to distinguish P and S waves from station records Suwa et al., 2010;Dammeier et al., 2011;Feng, 2011;Hibert et al., 2014). The onset of a landslide seismic signal is generally abrupt. Then the seismic amplitude increases gradually above the ambient noise level to peak ground motion, exhibiting a cigar-shaped envelope. After the peak amplitude, most of the landslide-generated seismic signals have relatively long decay times, on average about 70% of the total signal duration (Norris, 1994;La Rocca et al., 2004;Suriñach et al., 2005;Deparis et al., 2008;Schneider et al., 2010;Dammeier et al., 2011;Allstadt, 2013). In the frequency domain, landslide-induced seismic energy is mainly distributed below 10 Hz, with a triangular signature in a spectrogram, due to an increase over time in high-frequency constituents (Suriñach et al., 2005;Dammeier et al., 2011). The triangular signature in the spectrogram is the distinctive property that readily distinguishes landslide- However, this study currently focused on constructing and compare the rainfall thresholds for landslide warning, the traditionally statistical methods to estimate rainfall threshold were chosen. Time lag between rainfall history and soil saturation process was not considered in the study. 8. P4 L29: I think the chosen method can be shortly developed here. R: Thanks for t your suggestion. The detailed content of locating method has been added to the text as follows: "…. Locations were estimated with a cross-correlation method that could maximize tremor signal coherence among the seismic stations. The criteria of the stations chosen were their geographic distribution and tremor signal-to-noise ratios. The interpreted signals were treated with an envelope function to process cross-correlations analysed from different station pairs. Centroid location estimates were obtained by cross-correlating all station pairs and performing the Monte Carlo grid search method (Wech and Creager, 2008). While traditional methods seek the source location that minimizes the horizontal time difference between predicted travel time and peak lag time, this method seeks to minimize the vertical correlation distance between the peak correlation value and the   Table S1.
In the study, seven-days antecedent rainfall was considered as a rainfall parameter. The effect of antecedent rainfall should decay with time. Therefore, decay rate of antecedent rainfall with day was used to estimate effective rainfall. According to the decay rate, 0.7, the effect of antecedent rainfall with counting days longer than 7 days is slight. In the study, we adopt seven-days antecedent rainfall to estimate effective rainfall. 11. P5 L6: How can you consider the topographic, orographic effects? R: We appreciate the comments. We tested the rainfall data used in the study to validate the influence of distance and topographic effect on rainfall distribution. The effect of rain gauge distribution over the accuracy of rainfall has been assessed using gauge observation in a 35 km × 50 km region of south Taiwan (Fig. S2).

P5 L10: 100km² is already large catchment.
R: The effect of station distance has been tested to variation of rainfall. The errors of daily rainfall between the central point and the nearest rain gauge station (01V040) were smaller than 10 % (0.5%-10% at different date). Besides, the correlation coefficients would keep at 90% as a distance between the central point and rain gauge stations less than 20 km, and even keep at 98% as a distance less than 10 km (Fig. S3).
Therefore, in the study, an upper limit of basin area smaller than 100 km 2 (10 km × 10 km was adopted to avoid a significant decrease of the accuracy of rainfall. Because the density of rainfall stations in mountainous area would significantly decreases, the number of usable rainfall stations may be limited. The size of catchment area of 100km² is the upper limit for choose rainfall station. In practice, we chose the closest rainfall station. 13. P5 L2: rain event = typhoon? R: Yes. The sentence has been revised as below.

Distance between rain gauge and the central point of testing area (km
"In the study, hourly rainfall data were collected from the records of rain gauge stations (Fig. 2a). The major rainfall events analysed in the study were typhoon events. The distribution of precipitation during typhoon events is usually closely related to the typhoon track and the position of the windward slope, also as known as the orographic effect.…." property. In some cases, in-situ steel cables or closed-circuit television recorded the time information. This information was applied to the rainfall data analysis and then used to compare the rainfall conditions of the large landslides"

P6 L15: EQ1 cohesion here is only considered for a discontinuity (C = 0)? Or
for the specific material? R: We thanks reviewer's recommendation. Well development of detachment plane (e.g., sliding surface between sedimentary layers, connected joints, weathered foliation, etc.) have been widely considered as one important geological condition to induce a large landslide. Therefore, in the study, the C' of the detachment plane is simply assumed as the value of zero to behave the critical situation of slope stability. Cohesion in equation (1) is not considered for a specific material. The illustration of C' has been modified in the text as below.
"…Good development of a detachment plane (e.g., sliding surface between sedimentary layers, connected joints, and weathered foliation) has been widely considered as the geological condition under which a large landslide occurs (Agliardi et al., 2001;Tsou et al., 2011). Therefore, in this study, the c' of the detachment plane is simply assumed to be zero to represent the critical situation of slope stability." . The paragraph will be modified to avoid confusion. We did not calculate landslide seismic magnitude in the study due to the lack of a standard method for estimating landslide seismic magnitude so far.

P8 L4: what about SSL? R:
Most of the small landslides have strong instantaneous rainfall intensity. This means that a short duration and heavy rainfall can easily trigger small landslides.

Discussion:
The discussion is interesting because it puts the results in perspective. Nevertheless, some points have to be clarify.

5.2. The authors mention the fact that landslides occurred several types of
rocks with different geotechnical behaviors, but the chosen geotechnical parameters (table 1) are identical. Why? R: The main research purpose of this study was to establish a rainfall warning threshold which is applicable for large landslides, so a relatively simple but effective method was adopted. In this method, Keefer (1987) assumes that there is a potential sliding surface for these landslides, and the depth of the large-scale landslides are often deep to the strata. Therefore, although the movements of the soil material are not completely the same, under this assumption, it can still reach a considerable good effect.
In order to improve the Qc threshold, the critical volume of water, Qc, for each large landslide was estimated based on its slope gradient and depth (estimated by the equation: Z = 26.14A 0.4 ; Z: depth, m; A: disturbed area, m 2 ). Following the equation (4)    24. Fig. 4. Maybe with the topography visible on the map? R: Thank you for your suggestion. We had tried added topography in the fig. 4a. However, so many information made visually chaotic. Fig. 7. A) Is there only 1 event for the lowest limit? R: Yes. The figure will be removed in modified version.

Introduction
In recent years, the frequency of extreme rainfall events has increased globally, as has the number of large-scale natural disasters (Tu and Chou, 2013;Saito et al., 2014). These large-scale natural disasters (e.g., landslides, floods, etc.) cause both huge economic losses and human casualties. In mountainous areas, large-scale landslides (LSLs) can change the landscape 30 and erosion processes as well. Several previous studies have reported that the characteristics of a large-scale landslide may include (1) extremely rapid mass movement, (2) huge landslide volume, and (3) deep-seated excavation into rock formations (Chigira and Kiho, 1994;Lin et al., 2006). However, the discrimination of large-scale and non-large-scale landslides is still indistinctchallenging. In practice, the velocity of mass movement and depth of excavation are both difficult to measure, so the landslide area is commonly regarded as an indicator of the scale of a landslide. Although the occurrence frequency of 35 LSLslarge landslide is lower than that of non-large-scale landslides, known as small-scale landslides (SSLs), LSLs, large landslides cause rapid changes in the landscape, and the scale of LSL-induced disasters induced by large landslides is greater than that of SSLssmall landslides. Therefore, in this study, a landslide that disturbed an area larger than 0.1 km 2 is considered a large-scale landslide, while one not meeting this criterion is considered a small-scale landslide. It is well known that rainfall plays a significant role in the occurrence of landslides, so thorough understanding of the influences of different rainfall factors 2 is necessary. To reduce losses, the critical rainfall conditions that trigger LSLslarge landslides must be identified so that a rainfall threshold can be used as a forecast model to execute disaster prevention and mitigation measures.
In past research, it was difficult to estimate the threshold of precipitation convincingly due to the lack of accurate information on the occurrence times of landslides. Recent studies in geophysics (Kanamori et al., 1984;Surin �ach et al., 2005;Lin et al., 5 2010;Ekström and Stark, 2013;Chao et al., 2016;Chao et al., 2017) have suggested that the mass movement of large-scale landslides may generate ground motion. If such ground motion is recorded by seismic stations, the occurrence times of largescale landslides can be extracted from the records. In one case study, the rainfall that triggered the Xiaolin landslide, a giant landslide in southern Taiwan that disturbed an area of ~2.6 km 2 and resulted in more than 400 deaths in August 2009, was examined. It was found that if the occurrence time of the landslide was unknown,In general, if the exact occurrence time of a 10 landslide cannot be investigated, the time point with the maximum hourly rainfall will be conjectured as the occurrence time of the landslide (Chen et al., 2005;Wei et al., 2006;Staley et al., 2013;Yu et al., 2013;Xue et al., 2016). It was found that the time error between the conjectured and exact times would be 13 hours, which would result in an erroneous cumulated rainfall measurement of 513.5 mm (Fig. 1). However, with the assistance of seismic records, the time information for estimating critical rainfall can be acquired. 15 This study attempts to determine the occurrence times of landslides by identifying landslide-generated seismic signals to construct rainfall thresholds, and to clarify which thresholds are more suitable for triggering different warnings for small and large landslides. By applying various rainfall factors into statistical analysis, a statistical threshold can be built to explore the critical rainfall conditions of landslide occurrences, such as using rainfall intensity and duration to define rainfall threshold 20 curves (Caine, 1980;Guzzetti et al., 2008;Saito et al., 2010;Chen et al., 2015). Those rainfall thresholds provide valuable information for disaster prevention and mitigation. In this study, we used seismic data recorded by the network of the Broadband Array in Taiwan for Seismology (BATS) (Fig. 2a) and landslide maps generated from satellite images were used to obtain the exact occurrence times and locations of LSLs.large landslides. From these, we developed the rainfall threshold for LSLslarge landslides in Taiwan was developed. Moreover, located at the junction of the Eurasian plate and the Philippine 25 Sea plate, Taiwan has frequent tectonic activity (Ho, 1986;Yu et al., 1997;Willett et al., 2003). Fractural geological conditionsFractured rock mass coupled with a warm and humid climate, and an average of 3 to 5 typhoon events per year, contribute to the high frequency of slope disastersfailures in mountainous areas in Taiwan (Wang and Ho, 2002;Shieh, 2000;Dadson et al., 2004;Chang and Chiang, 2009;Chen, 2011). The high coverage of the seismic network and rain gauge stations in Taiwan, coupled with the high occurrence frequency of landslides, make the island a suitable area for examining the use of 30 seismic observations to identify landslide occurrence times and thus the rainfall factors contributing to landslide events.

Large-scale landslide mapping
To determine the locations and basic characteristics of LSLslarge landslides occurring in the years 2005-2014, the landslide areas across the entire island of Taiwan were interpreted using SPOT-4 satellite remote sensing images with a spatial resolution 35 of 10 m in multispectral mode. Images with minimal cloud cover were selected from pre-and post-typhoon and heavy rainfall events. All images were orthorectified to a standard base image and checked manually using fixed visible markers to ensure spatial consistency over time. Figures 2b and 2c show synthetic SPOT images that were used to identify landslides triggered by Typhoon Morakot in 2009. Bare areas are visibly distinguishable in the SPOT images.
The Normalized Difference Vegetation Index (NDVI) was used to conduct a preliminary classification of bare areas . The exact NDVI thresholds for bare areas differed from one image to another and were determined by tuning the cut-off value based on visible contrasts. After image interpretation, classified areas were clustered based on slope using a digital elevation model with a resolution of 40 m to identify bare areas not associated with landslides (e.g., roads and buildings).
The results of the interpretation were compared with a 1:5000 topographic map to exclude areas of interpretation misjudgement, 5 such as fallow farmland or alluvial fans. Landslides induced specifically by a rainstorm eventevents were distinguished by overlaying the pre-and post-event image mosaics. Based on the definition and description of deep-seated gravitational slope deformation (DSGSD) and large landslides (Lin et al., 2013a;Lin et al., 2013b), a large landslide should possess three characteristics: 1) a depth larger than 10 m, 2) a volume greater than 1,000,000 m 3 , and 3) a high velocity. In practice, it is difficult to confirm these three characteristics without in-situ investigation and geodetic survey. Therefore, a disturbed area of 10 100,000 m 2 was determined as an accommodating indicator to sort large landslides from small landslides. Finally, LSLslarge and SSLssmall landslides were distinguished and classified according to the criterion of an affected area of 0.1 km 2 . In this study, the types and mechanisms of individual landslides were not investigated, but landslide area was used as the main factor for investigating the different rainfall conditions that trigger LSLslarge and small landslides.

Interpretation of ground motions induced by large-scale landslides 15
The movement of a landsliding mass has several different motion processes, such as sliding, falling, rotation, saltation, rolling and impacting. These complex motion processes act on the ground surface to generate ground motion (Kanamori et al., 1984;Ekström and Stark, 2013). When this ground motion is recorded by adjacent seismic stations, the landslide-related pattern in a spectrogram develops a triangular time/frequency signature in the 1-10 Hz frequency band (Suriñach et al. 2005;Chen et al. 2013).The seismic wave generated by a landslide can be attributed to the shear force and loading on the ground surface as the 20 mass moves downslope. Many studies have shown that the source mechanism of a landslide is highly complicated, and that its seismic waves mainly consist of surface waves and shear waves, making it difficult to distinguish P and S waves from station records Suwa et al., 2010;Dammeier et al., 2011;Feng, 2011;Hibert et al., 2014). The onset of a landslide seismic signal is generally abrupt. Then the seismic amplitude increases gradually above the ambient noise level to peak ground motion, exhibiting a cigar-shaped envelope. After the peak amplitude, most of the landslide-generated seismic signals have 25 relatively long decay times, on average about 70% of the total signal duration (Norris, 1994;La Rocca et al., 2004;Suriñach et al., 2005;Deparis et al., 2008;Schneider et al., 2010;Dammeier et al., 2011;Allstadt, 2013). In the frequency domain, landslide-induced seismic energy is mainly distributed below 10 Hz, with a triangular signature in a spectrogram, due to an increase over time in high-frequency constituents (Suriñach et al., 2005;Dammeier et al., 2011). The triangular signature in the spectrogram is the distinctive property that readily distinguishes landslide-induced signals from those of earthquakes and 30 other ambient noise.
In this study, a total of nineteen rainstorm events (seventeen typhoon-induced events and two heavy rainfall events) in the years 2005-2014 were selected to examine the seismic records (Table S1). The seismic data during typhoons and heavy rainfall events having cumulated rainfall exceeding 500 mm from 2005 to 2014 were collected, and the seismic signals of local 35 earthquakes, regional earthquakes, and teleseismic earthquakes were excluded based on the earthquake catalogues maintained by the United States Geological Survey and the Central Weather Bureau, Taiwan. After the removal of instrument response, mean, and linear trends, a multitaper method (Percival and Walden, 1993;Burtin et al., 2009) was employed for spectral analysis of the continuous seismic records. A 5-min moving window with 50% overlap of the seismic records provided a good spectrogram in the frequency range of 1-10 Hz. Eventually, landslide-related triangular signatures in the spectrograms were 40 manually identified to find the characteristic signals generated by landslides (Fig. 3a, 3b). To reduce the uncertainty caused by the artificial method ofmanual identification, only events with very obvious triangular signatures in the spectrograms (e.g. Fig.   S1) were used to examine rainfall statistics in this study.
The detection of the occurrence time of landslide-induced ground motion is a substantial key to this study. In seismology, many methods can be used to detect the appearance of the seismic signals of earthquakes, and one of the most widely used 5 methods is the STA/LTA ratio (Allen, 1978). For landslides, the duration of landslide-induced signals usually ranges from tens to hundreds of seconds (Helmstetter and Garambois, 2005;Chen et al., 20132013a). As compared with the current widelyused rainfall data recorded once per hour, the duration of landslide-induced seismic signals is significantly short. Thus, to avoid misjudgements caused by different signal-detection methods or manual interpretation, this study adopted the time of the maximum amplitude of the envelope of the vertical-component signal recorded in the station closest to the landslide as the 10 occurrence time of the landslide. Considering the transmission speed of seismic waves, a time difference of several seconds to several tens of seconds was negligible with respect to the sampling rate of rainfall records.
To determine which landslides generated ground motion, it was necessary to locate the seismic sources of the signals. However, the arrival times of the P-and S-waves of landslide-induced ground motion could not be clearly distinguished. As a result, a 15 locating approach proposed by Chen et al. (20132013a) and Chao et al. (2016) was adopted in this study to locate the landslideinduced signals. TheLocations were estimated with a cross-correlation method was used to calculate the correlations between the envelope functions of the that could maximize tremor signal coherence among the seismic signals received by different seismic stations,. The criteria of the stations chosen were their geographic distribution and subsequently the seismic sources were located with tremor signal-to-noise ratios. The interpreted signals were treated with an envelope function to process 20 cross-correlations analysed from different station pairs. Centroid location estimates were obtained by cross-correlating all station pairs and performing the Monte Carlo grid search method (Wech and Creager, 2008). While traditional methods seek the source location that minimizes the horizontal time difference between predicted travel time and peak lag time, this method seeks to minimize the vertical correlation distance between the peak correlation value and the predicted correlation value.

25
Finally, the location results of landslide-induced seismic signals were compared with the exact locations of LSLslarge landslides interpreted from satellite images (Fig. 3c, 3d). If the locations matched, the occurrence times of the landslides could be obtained, and the time information could be applied to rainfall data analysis.

Analysis methods of statistically-based rainfall threshold for landslides
In the study, hourly rainfall data were collected from the records of rain gauge stations (Fig. 2a). The major rainfall events 30 analysed in the study were typhoon events. The distribution of precipitation during typhoon events is usually closely related to the typhoon track and the position of the windward slope, also as known as the orographic effect. In addition, the density and distribution of rainfall stations in mountainous areas directly affect the results of rainfall threshold analysis. If the landslide location and the selected rainfall station are located in different watersheds, the rainfall information is unlikely to represent the rainfall conditions for the landslide. In some cases, however, the diameter of the typhoon was so large that the orographic 35 effects could be ignored (Chen and Chen, 2003;Sanchez-Moreno et al., 2014) Therefore, in this study, the selection criteria for a rainfall station were that the rainfall station must be located within the same watershed as the landslide, and at the shortest straight distance from the landslide; moreover, the watershed must be smaller than 100 km 2 in area to ensure that the records at rain gauge stations were sufficient to represent the rainfall at the landslide locations.

40
These criteria were established after testing the influences of distance and topographic effects on rainfall distribution (see supporting information S3). In rainfall analysis, the beginning of a rain event is defined as the time point when hourly rainfall exceeds 4 mm, and the rain event ends when the rainfall intensity remains below 4 mm/h for 6 consecutive hours. The critical rainfall condition for a landslide was calculated from the beginning of a rain event to the occurrence time of the landslide. (Jan and Lee, 2004;Lee, 2006). In this way, average rainfall intensity (mm/h), cumulated rainfall (mm), and rainfall duration (h) for each LSLlarge landslide could be used as the factors in the rainfall threshold analysis. In addition to the three factors mentioned above, the daily rainfall for the seven days preceding the rainstorm was considered as antecedent rainfall. (Ra). The 5 antecedent rainfall (Ra) was calculated with a temporal weighting coefficient of 0.7, with the weight decreasing with days before the event. The formula was = ∑ 0.7

=1
× , where is the daily rainfall of the i th day before the rainfall event.
The sum of antecedent rainfall and principal event rainfall was regarded as the total effective rainfall (Rt). This definition of a rain event has been officially adopted in Taiwan (Jan and Lee, 2004). The use of different definitions of a rain event would result in differences in statistical rainfall conditions, but the statistical criteria used in this study ensured the consistency of 10 data processing in the critical rainfall analysis.
Based on different rainfall factors, three common rainfall threshold analysis methods were used in the study. The first method was the I-D method, with the power law curve, I = aD -b , where a is the scaling parameter (the intercept) of the threshold curve and b is the slope (the scaling exponent) (Caine, 1980;Wieczorek, 1987;Keefer et al., 1987). In this study, the I-D rainfall 15 threshold curve at 5% exceedance probability was estimated by the method proposed by Brunetti et al. (2010). This threshold was expected to leave 5% of the data points below the threshold line. The second method was the rainfall-based warning model proposed by Jan and Lee (2004), which is based on the Rt and I product values. With the I-Rt-I method, rainfall intensity and cumulated rainfall were plotted and used to calculate the cumulative probability of the product value of I and Rt by the Weibull distribution method (Jan and Lee, 2004). The cumulative probability of 5% of Rt and I product values was taken as the I-Rt-I 20 rainfall threshold. The third method was the Rt-D method (Aoki, 1980;Fan et al., 1999). In the Rt-D method, the 5% cumulative probability of the product value of Rt and D by the Weibull distribution method was taken as the Rt-D rainfall threshold.
In addition to that of LSLslarge landslides, the time information of 193 small-scale landslides, such as shallow landslides and debris flows, from the years 2006-2014 was collected from the annual reports of debris flows investigated by the Soil and 25 Water Conservation Bureau (SWCB) of Taiwan., but it was not extracted from seismic records. Most of the 193 small landslides caused disasters and loss of life and property. In some cases, in-situ steel cables or closed-circuit television recorded the time information. This information was applied to the rainfall data analysis and then used to compare the rainfall conditions of the LSLslarge landslides.

Critical volumeheight of water modemodel 30
Whether a given slope will produce a landslide depends on the balance between the shear strength of the slope material and the downslope component of the gravitational force imposed by the weight of the slope material above a potential slip surface.
A critical volumeheight of water model proposed by Keefer et al. (1987) was used in this study to construct a rainfall threshold.
The model was derived from existing slope stability theory with some simplifying assumptions. The shear strength of the material at a point within a slope is expressed as: 35 where , is effective cohesion of material, is total stress perpendicular to the potential sliding surface, is pore water 40 pressure, and , is effective friction angle of slope material. The main cause of a slope disasterfailure is the infiltration of rainfall into the slope and accumulation above the impermeable layer, which increases the pore water pressure of the slope material. As the pore water pressure ( ) increases, the shear strength ( ) decreases, eventually leading to slope failure. A critical value of pore water pressure exists in each slope, assuming an infinite slope composed of a non-cohesive sliding surface ( , =0). The pore water pressure threshold can be calculated as: , 5 (2) where Z is the vertical depth of the sliding surface, is the unit weight of the slope material, and is the slope angle. Good development of a detachment plane (e.g., sliding surface between sedimentary layers, connected joints, and weathered foliation) has been widely considered as the geological condition under which a large landslide occurs (Agliardi et al., 2001;Tsou et al., 10 2011). Therefore, in this study, the c' of the detachment plane is simply assumed to be zero to represent the critical situation of slope stability.
As the pore water pressure w increases to the pore water pressure threshold , a critical volumeheight of water is retained above the sliding surface until the initiation of slope failure. The is calculated as: 15 where is the critical value of pore water pressure, is the unit weight of water, and is the effective porosity, which 20 is the residual porosity of the slope material under free gravity drainage. The drainage rate of a saturated zone is represented by the average value I0, the unit of which is mm/h. In a heavy rainfall event, the critical quantity of water for causing a slope disasterfailure is defined as:

Topographic features of large-scale landslides
The satellite imagery interpretation showed that, from 2005 to 2014, a total of 686 landslide events with areas greater than 0.1 30 km 2 occurred in mountainous areas of Taiwan (Fig. 4a). Most of these LSLslarge landslides had areas of 0.12 to 0.15 km 2 , and their slope angles before the landslides occurred were concentrated between 30° and 40° (Fig. 4b). The number of landslides occurring on slope angles exceeding 40° slightly increased after 2010. ThisAlthough the increase was quite slight, it was most likely due to the fact that during the extremely heavy rainfall of Typhoon Morakot in 2009, more than 2,0002000 mm precipitated in four days, causing numerous a large number of landslides on lowerand exhausting many unstable slopes and 35 reducing the stability of the (Chen et al., 2013b). Consequently, landslides occurred on steeper slopes in the following years.
The LSLslarge landslides were primarily concentrated on slopes with elevations ranging from 500 m to 2000 m (Fig. 4c), but the distributions of the highest and lowest elevations of these LSLslarge landslides showed that thetheir average vertical displacement of these LSLs was greater than 500 m.

7
The location information of the 193 small-scale landslides investigated by the SWCB was used to obtain the topographic features of the SSLssmall landslides as well. The distribution of the slope angles of the SSLsthese landslides was similar to that of the LSLs.large landslides. However, the distribution of the elevations of the SSLssmall landslides was quite different from that of the LSLs.large landslides. Unlike those of the LSLslarge landslides, a large portion of the elevations of SSLssmall landslides was concentrated at about 1000 m. Although the difference in elevation distribution between LSLslarge and 5 SSLssmall landslides seems to indicate that the topographic features of LSLslarge landslides were relatively more widespread than those of SSLssmall landslides, the situation should be attributed to the limited in-situ investigations of the SWCB.
Currently, the vast majority of landslides still cannot be investigated in the field.

The critical rainfall conditions for triggering LSLslarge landslides
Comparison of the location solutions of seismic signals and the landslide distribution map revealed that the matched LSLs 10 large landslides had deviations in distance of 0 to 20 kilometerskilometres. In addition to distance, the resultant traces of two horizontal-component signals could be plotted. The direction of the resultant trace of a given landslide-induced seismic record with the slope aspect in the vicinity of the located point could be compared so as to eliminate the irrelevant landslides, those which had slope aspects different from the signal traces. The ground motion traces of the signals were alsohad to be correlated with the directions of movement of the landslides to reconfirm the matched LSLs.large landslides. In total, 62 LSLslarge 15 landslides were paired successfully with seismic record locations (Fig. 2a, Table S2). These 62 LSLslarge landslides were distributed in watersheds with high cumulated rainfall during heavy rainfall events. In addition, the 62 LSLslarge landslides were verified by satellite images from multiple years to guarantee that the shapes and positions were highly credible.
Subsequently, the occurrence times of these 62 LSLslarge landslides were obtained from seismic signals.

20
The time information was used to implement rainfall analysis. About two-thirds (41) of the LSLslarge landslides occurred when the total effective rainfall exceeded 1000 mm (Fig. 5). The statistical results of rainfall intensities at the times of LSLlarge landslide occurrences showed that more than half of the LSLslarge landslides occurred when the rainfall intensity was less than 20 mm/h. Only seven of the LSLslarge landslides occurred when the rainfall duration was less than 24 hours, and the rainfall durations of these seven events all exceeded 10 hours. The results of single rainfall-factor analysis indicated that the 25 effects of rainfall duration and cumulated rainfall were much more remarkable for LSLslarge landslides than for SSLssmall landslides, and that the rainfall intensity at the time of landslide occurrence was not the main factor influencing LSLs.large landslides. Therefore, the average rainfall intensity was adopted for the following multi-factorial analyses.

Dual rainfall-factor analysis of I-D, I-Rt, and Rt-D thresholds 30
The single rainfall-factor analysis indicated that there was no significant correlation between landslides and rainfall intensity at the time of LSLlarge landslide occurrences. In the dual rainfall-factor analysis, the I-D rainfall threshold was assessed by using the average values of rainfall intensity and rainfall duration. The obtained I-D rainfall threshold was I = 71.9D -0.47 (D > 24 h) (Fig. 6a). We also compared theThe rainfall information obtained from SSLssmall landslides that were reported by the SWCB from 2006 to 2014 was also compared, and the I-D rainfall threshold curve for LSLslarge landslides also fit the lower 35 boundary of the rainfall conditions of SSLs.small landslides. In addition, the distribution of the rainfall durations indicated that the SSLssmall landslides were distributed evenly from 3 to 70 hours, while the LSLslarge landslides were mostly distributed above 20 hours. The rainfall intensity, however, could not be used effectively to distinguish these two kinds of slope disastersfailures. Even under the same rainfall duration, the rainfall intensities of many SSLssmall landslides were higher than those of LSLslarge landslides. This result sufficiently demonstrated that rainfall intensity could not be used to distinguish 8 between SSLssmall landslides and LSLslarge landslides. Therefore, the I-D rainfall threshold may not allow assessment of the landslide scale. It was also found that most of the LSLslarge landslides with larger areas were concentrated in rainfall durations of more than 50 hours, but the average rainfall intensity was not well-correlated with landslide area. The average rainfall intensity of the SSLssmall landslides was very high for short durations, but the average duration of the SSLssmall landslides was much lower than that of LSLs.large landslides. Therefore, continuous high-intensity rainfall incurs a high 5 likelihood of LSLlarge landslide occurrence.
We also compared theThe I-D rainfall thresholds obtained in the study were also compared with those of previous studies that focused on shallow landslides or debris flows. This comparison revealed that the I-D threshold curve for LSLslarge landslides was much higher than the threshold curves for shallow landslides or debris flows. 10 Based on the analysis of the relationship between total effective rainfall (Rt) and rainfall duration (D), the product of Rt and D for LSLslarge landslides with a cumulative probability of 5% was 12,773 mm·h (Fig. 6b), and the rainfall threshold was also much higher than the 5% cumulative probability of SSLssmall landslides (487 mm·h). Total effective rainfall differed considerably between LSLslarge and SSLs.small landslides. Most SSLssmall landslides had a total effective rainfall below 15 500 mm, whileand only a few SSLs occurred when total effective rainfall exceeded 1000 mm. The landslide size groups shifted from small landslides for relatively short duration and low effective rainfall to large landslides for long duration and very large effective rainfall. As a result of the disparity in the Rt-D threshold curves for LSLslarge and SSLssmall landslides, it was determined that Rt-D analysis could be used effectively to distinguish SSLssmall landslides from LSLslarge landslides.

20
The analysis of the relationship between average rainfall intensity (I) and total effective rainfall (Rt) revealed that the product value of both factors for 5% cumulative probability was 5,640 mm 2 /h (Fig. 6c). The Rt-I threshold curve for LSLslarge landslides was not much higher than that for SSLssmall landslides (1,541 mm 2 /h). Combining the results of the three kinds of dual-factor rainfall threshold analyses revealed that the critical rainfall conditions for SSLssmall landslides included high average rainfall intensity but relatively low cumulatedeffective rainfall, while those for LSLslarge landslides included long 25 rainfall duration and high effective cumulated rainfall. These results corresponded well with the former theoretic expectation (Van Asch et al., 1999;Iverson, 2000).
The main mechanism of shallow landslides is heavy rainfall along with rapid infiltration, causing soil saturation and a temporary increase in pore-water pressure. However, prolonged rainfall also plays an important role in slow saturation, which 30 in turn influences the groundwater level and soil moisture, and causes LSLs.large landslides. These facts have been recognized in many studies around the world (Wieczorek and Glade, 2005;Van Asch et al., 1999;Iverson, 2000), but they have been analysed in only a few locations (e.g., a mountainous debris torrent, a shallow landslide event, and an individual rainfall event). Using the regional dataset of landslides and the times information, this study identified the critical rainfall conditions for LSLslarge and SSLssmall landslides in Taiwan. 35

The critical volumeheight of water model for forecasting LSLlarge landslides
The critical height of water, , on a sliding surface for each large landslide was estimated based on its slope gradient, depth (estimated by the equation Z = 26.14A 0.4 ; Z: depth in m; A: disturbed area in m 2 ), and the geological material parameters of the study area (Table 1) were used to calculate the critical volume of water on the sliding surface, which was found to be 40 452 mm.). The value was inserted into = ( − 0 ) • to obtain an 0 value offor each large landslide. For the 62 detected landslides, the cumulative probability of 5% of the and I0 values was taken as the critical value. The critical value of I0 was 1.04 mm/h5, the critical was 430.2, which is more suitable for LSLslarge than for SSLssmall landslides, and the threshold curve was rewritten as (I -1.045)•D = 452430.2. The application of this threshold curve to average rainfall intensity and rainfall duration showed that almost all the LSLslarge landslides could have been forecasted. This application demonstrated a good function as a LSLlarge landslide forecast model (Fig. 6d). In addition, the threshold curve can be used to distinguish LSLslarge landslides and SSLssmall landslides clearly. This advantage can prevent or reduce false forecasts. The 5 critical volumeheight of water model combines statistical and deterministic approaches for the assessment of critical rainfall. Therefore, the parameters used to calculate can be adjusted based on regional geologic and topographic environments within a specific area. The model illustrates the importance of the cumulative volume of water and rainfall duration to LSLslarge landslides and takes into account the effects of both infiltration of water and average rainfall intensity. The critical hydrological conditions for LSLslarge landslides, a long duration and a high amount of cumulated rainfall, can be determined 10 as well.
In general, physically-based models are easy to understand and have high predictive capabilities Wieczorek, 1995: Salciarini andTamagni, 2013;Papa et al., 2013;Alvioli et al., 2014). However, they depend on the spatial distribution of various geotechnical data (e.g., cohesion, friction coefficient, and permeability coefficient), which are very difficult to obtain. 15 Statistically-based methods can include conditioning factors that influence slope stability, which are unsuitable for physicallybased models. Statistically-based models rely on good landslide inventories and rainfall information. In this study, the threshold for a large landslide was estimated based on a mixture of physically-and statistically-based methods. Unlike other physically-based I-D thresholds, which are commonly constructed based on artificial rainfall information for shallow landslides (Salciarini et al., 2012;Chen et al., 2013c;Napolitano et al., 2016) (Table S3), the threshold proposed in this 20 study seemed to be higher and more suitable for large landslides (Fig. 6d).
Although the geological and rainfall conditions in Taiwan and in other countries are not the same, seismic records can be used to obtain the time information of landslide occurrences for rainfall threshold analysis in other countries. For countries with geological and rainfall conditions similar to those of Taiwan (e.g., Japan and the Philippines)() (Saito and Oguchi, 2005;25 Yoshimatsu and Abe, 2006;Evans et al., 2007;Yumul et al., 2011), the results of this study may serve as a useful reference for the development of a forecast model for rainfall-triggered landslides.

InfluenceApplication of Typhoon Morakot in 2009 on the rainfall thresholds for LSLs
A previous study has pointed out that because Typhoon Morakot in 2009 was an extreme rainfall event that resulted in 486 30 large-scale landslides in Taiwan, the surface erosion caused by the typhoon was equivalent to 20 years of accumulated erosion (Chen et al., 2013). Comparison of the data on the rainfall that triggered the LSLs in 2005-2008 with that in 2010-2014 (To verify the usability of the rainfall thresholds proposed in this study, Typhoon Soudelor of 2015 was chosen to demonstrate the early warning performance. Typhoon Soudelor was one of the most powerful storms on record. It generated 1400 mm of rainfall in northeastern Taiwan and almost 1000 mm of rainfall in the southern mountainous area of Taiwan (Wei, 2017;Su et 35 al., 2016). After the seismic signal analytical procedure, the occurrence time, 2015/8/8 18:59:50 (UTC), of a large landslide (named the Putanpunas Landslide) located in southern Taiwan was obtained (Fig. 7). The seismic signal generated by the Putanpunas Landslide was also detected by Chao et al. (2017). The seismic signals generated by this large landslide could be identified from six BATS stations, and the distance error was less than 6 km. The rainfall records of rain gauge station C1V190, which was situated in the same watershed and 14.6 km away from the large landslide, were collected for rainfall analysis. 40 Typhoon Soudelor made landfall in Taiwan on August 7, 2015, and dropped a cumulated rainfall of 546 mm and had a maximum rainfall intensity of 39 mm/h on August 8 at rain gauge station C1V190 (Fig. 8). The rainfall event began at 22:00 August 7 and last for 26 hours, and the Putanpunas Landslide initiated at the 22nd hour. This landslide occurred when the rainfall intensity was on the decline.
Regarding landslide early warning using rainfall thresholds, once the rainfall conditions at a given rainfall station exceed the 5 rainfall thresholds for triggering landslides, the slopes located within the region of the rainfall station will have high potential for failure. Based on the statistically-based I-D threshold for small landslides, a small-landslide warning would have been issued at the sixth hour of the rainfall event (Fig. 8). The long interval of sixteen hours between the warning and the occurrence time of the Putanpunas Landslide could have reduced the reliability of the warning or even caused the warning to be considered a false alarm. Therefore, it is essential to establish different thresholds for landslides of different scales. Using the I-Rt threshold 10 (i.e., Rt·I= 5,640), a large-landslide warning would have been issued at the ninth hour of the rainfall event (i.e., thirteen hours before the Putanpunas Landslide occurred). According to the statistically-based I-D threshold for large landslides, a landslide warning would have been issued at the same hour as the I-Rt threshold. In addition, a warning based on the Rt-D threshold  However, due to the limited amount of LSL rainfall data, the slight difference in rainfall thresholds is still difficult to view as solid evidence in support of the decline in critical rainfall conditions for triggering LSLs. 25

Rainfall thresholds for different rock types
Among the 62 LSLs, 23 LSLs were located in slate, 23 LSLs occurred in schist, 11 LSLs occurred in interbedded sedimentary rocks, and 5 LSLs were located in meta-sandstone. From the relationship between total effective rainfall and rainfall duration ( Fig. 8), it was found that the critical Rt for schist was the lowest. Schist is a kind of foliated metamorphic rock that is prone to abundant crack propagation along with sudden loss of cohesion. The cracks in the rock mass become both a path for water 30 infiltration and the interface of rock mass separation or collapse. By contrast, the critical value of Rt for metamorphic sandstone is relatively higher. LSLs on meta-sandstone occurred only when Rt exceeded 500 mm. In comparison, schist LSLs occurred when Rt was lower than 500 mm. In general, meta-sandstone has a compact texture, which leads to high strength.
The main path of water infiltration into the ground is usually dense cracks generated in rocks. However, the differences in the 35 critical values of Rt for LSLs in different rock types are limited (Fig. 8). In addition, the rainfall data that could be used for developing rainfall thresholds for LSLs in each rock type are insufficient. Although we would like to discuss the influences of rock types on the occurrence of LSLs, it is obvious from the current data that the differences in critical rainfall between different rock types are not significant.

Limitation of seismic detection for LSLslarge landslides
The number of LSLslarge landslides detected from seismic records, 62, comprised only nine percent of the total LSLslarge landslides in 2005-2014 in Taiwan. This low percentage indicates that the vast majority of LSLslarge landslides were not well identified from seismic records. If this limitation can be surmounted, more time information on LSLlarge landslide occurrences can be used to develop rainfall thresholds. The average interstation spacing of the Broadband Array in Taiwan for Seismology  5 is around 30 km. A higher density of seismic stations would improve the detection function. In addition, to determine the limitation of LSLlarge landslide detection distance as a function of LSL large landslide-disturbed area, the most distant seismic station where LSLlarge landslide signals were visible was selected. Some previous studies have applied similar approaches to probe the detection limit (Dammeier et al., 2011;Chen et al., 20132013a). The relationship between the maximum distance of detection and the LSLlarge landslide-disturbed area shows a limitation of the detection distance due to the LSL'slarge 10 landslide's magnitude (Fig. 9). In Figure 9, each data point represents the distance between a landslide location and the most distant seismic station detecting it, as well as the landslide-disturbed area. In other words, when the distance between a seismic station and a landslide that has the same given landslide-disturbed area as the data is shorter than the value of the data, seismic signals induced by the landslide can be interpreted from the records of the seismic station. Therefore, a lower boundary of these data can be determined to demarcate an effective detectable region. As a LSL'slarge landslide's area increases, the 15 maximum distance between the LSLlarge landslide location and seismic detection increases. An upperA detection limit can be described by log( ) = 0.5069 * × log( ) -1.3443 Eq. , For a given LSL The boundary of detection was determined empirically based on the two lowest values of the farthest distance of detection (i.e., 31.0 km and 37.6 km) having disturbed areas of 1.6×10 5 and 1.2×10 5 m 2 . For a given large landslide, if a station is located below the upper detection limit, the seismic signal should be detectable. However, not all the stations located in detectable regions recorded clear LSLlarge landslide-induced seismic signals. One of the possible reasons is that the environmental 25 background noise affected the signal to noise ratio of the seismic records during heavy rainfall events. Therefore, the detection limit may also depend on the signal quality at each station.

Conclusion
In this study, seismic signals recorded by a broadband seismic network were used to determine the exact times of occurrence of large-scale landslides (LSLs),, and the rainfall threshold for LSLslarge landslides was assessed statistically based on the 30 time information. Based on the rainfall information of 62 LSLslarge landslides that occurred from 2005 to 2014 in Taiwan, the rainfall conditions for triggering LSLslarge landslides include total effective rainfall of more than 1000 mm and rainfall duration of more than 24 hours. After the rainfall thresholds were analysed by the I-D, Rt-D, and I-Rt-I methods, the rainfall thresholds based on different dual factors for triggering LSLslarge landslides were obtained. Furthermore, a critical water model combining statistical and deterministic approaches was developed to figure out a three-factor threshold for LSLs.large 35 landslides. The rainfall information and geologic/topographic parameters finally were applied to obtain the threshold curve, (I-1.045)·D = 452430.2, where average rainfall intensity I is in mm/h and rainfall duration D is in h. This new critical model can be used to improve the forecasting of LSLslarge landslides and will not lead to confusion between SSLssmall landslides and LSLslarge landslides. The influences of extreme rainstorm events and rock types on the rainfall threshold were also investigated. However, the changes in the rainfall thresholds for LSLslarge landslides either before or after an extreme event 40 or in different rock types were not notable.