The Inuence of Rainfall Amounts Not Exceeding Critical Rainfall on Landslide Occurrence in Japan

Critical rainfall events are used in landslide early-warning systems to predict the occurrence and severity of disasters. In this study, past landslide disasters in Japan were identied for which the critical rainfall set for each 1-km grid was exceeded using historical landslide records, radar-based rainfall data over a 1-km grid, and standard rainfall data collected over the past 17 years. It was determined that nearly equal numbers of rainfall events were identied with higher and lower rainfall amounts than the critical rainfall. The probability that a series of rainfall events would cause a landslide was approximately 1.15% when the critical rainfall was exceeded and 0.09% otherwise, a difference of approximately 10 times. It was also found that even if critical rainfall was not exceeded, in the case of debris ow and slope failures, there was rainfall that exceeded the standard rainfall one or two days before. In the case of landslides, there was rainfall that exceeded the critical rainfall one or two weeks before, and if the critical rainfall was exceeded in another rainfall event, a landslide could occur. The operational evaluation of Japanese LEWSs has a recall value of 0.486 as the accuracy of occurrence prediction, which was related to the fact that almost half of the rainfall events occurred in nonexceedance of the reference rainfall. The specicity was 0.935, known as the accuracy of nonoccurrence prediction, which was also greatly inuenced by the TN (true negative) data of nonexceeding rainfall events, which accounted for most of the data.


Introduction
Rainfall-induced landslides are important natural hazards and often cause considerable damage to society. To assess the primary causes of landslides, understanding the relation between rainfall and landslide occurrence is necessary. Many studies have focused on quantifying rainfall parameters to empirically derive critical rainfall to understand the regional propensities of landslide occurrences and to develop landslide early warning systems (LEWSs, see Piciullo et al. 2018, Guzzetti et al. 2020, for a detailed review). For example, the rst regional LEWS was constructed in Hong Kong in 1977 in response to catastrophic landslide events in 1972 and 1976 that caused many fatalities (Brand et al. 1984, Malone 1988). Since then, many regional LEWSs have operated in the USA (e.g., Wilson et al. 1993 (Osanai et al. 2010). These LEWSs have used many rainfall parameters, such as rainfall intensity, duration, cumulative rainfall, antecedent rainfall, and physical-based rainfall-runoff modes, based on ground rain gauges, weather radar, and satellite rainfall products.
These LEWSs assess the timing of landslides based on an empirical critical rainfall threshold. A key assumption of applying critical rainfall is that the likelihood of landslide occurrence increases with increasing rainfall amounts. However, the application of empirical critical rainfall for LEWSs has an inherent tradeoff relation between overestimation and underestimation with landslide occurrences under rainfall conditions of critical rainfall. Validation of the predictive performance of LEWSs is therefore important to improve LEWSs (Guzzetti et al. 2020). Although many studies have validated the LEWSs for Loading [MathJax]/jax/output/CommonHTML/jax.js past heavy rainfall events, no study has validated nationwide landslide events for entire 1-km grids over the long term.
Japan is located in the East Asian monsoon region. The Japanese archipelago is characterized by highrelief topography and complex geological conditions. Heavy rainfall frequently occurs in Japan, especially during the summer monsoon season, causing landslide disasters (Saito et al. 2014). Many studies have analyzed the relations between rainfall parameters and landslide occurrences. For example, early notions of Endo (1970) and Onodera et al. (1974) showed the critical rainfall for landslide occurrences using maximum hourly rainfall and cumulative rainfall. The rst nationwide LEWS was developed by the Ministry of Construction in 1984 using hourly rainfall, antecedent rainfall, and effective rainfall (Ministry of Construction 1984, Terada and Nakaya 2001). The Ministry of Land, Infrastructure, and Transport and Tourism in Japan (MLIT) and the Japan Meteorological Agency (JMA) has operated the current Japanese LEWS since 2005 using 60-minute rainfall and the Soil Water Index (SWI, an antecedent precipitation index) (Osanai et al. 2010, see Section 2). Although the Japanese LEWS has been operated for more than 15 years, few studies have validated its predictive performance. The predictive performance of the Japanese LEWS is addressed in this study by analyzing the nationwide landslide inventory (n > 15,000) between 2003 and 2020 (17 years) and rainfall data with a spatial resolution of 1 km or 5 km. In particular, this study focuses on the timing of landslides and underestimation of landslide occurrences in terms of the impacts of antecedent rainfall before landslides are induced by rainfall events. In addition, operational evaluation of the critical rainfall was also conducted.
The current Japanese critical rainfall that is used to identify occurrence and nonoccurrence setting methods uses the RBF network of Kuramoto et al. (2001) to set nonlinear critical rainfall (Fig. 1). The rainfall indices used are the 60-minute cumulative rainfall as the short-term rainfall index and the soilwater index, which is the sum of water depths of the three-layer tank model parameterized in a basin consisting of three typical geological classi cations in Japan (Okada 2005), as the long-term rainfall index. A three-dimensional PBFN output response surface is calculated for each 1-km grid based on the rainfall indices, and the response surface is subtracted from the highest value of the RBFN output to capture the landslide data for LEWS and used as a two-dimensional critical rainfall. As shown in (Osanai et al. 2010), the critical rainfall using RBFN is set for each grid, which re ects the characteristics of the primary factor in each grid, which is referred to here as the in-line method. In addition, nonexceeding rainfall of the critical rainfall was also considered in this paper to study the effect of antecedent rainfall of landslides that occur in small-scale rainfall.
The types of phenomena present in the Japanese landslide data will be explained in the next chapter. In current technical standards, debris ows and spatiotemporally concentrated slope failures (debris avalanches) are extracted from landslide data, and the critical rainfall is set for LEWS (Osanai et al. 2010). The types of phenomena in the Japanese inventory will be explained in the next chapter. Landslides and slope failures in small-scale rainfall were not included in the rainfall standard. In some parts of this study, two rainfall indices were used to express the rainfall scale of the three-dimensional Loading [MathJax]/jax/output/CommonHTML/jax.js PBFN output response surface and the RBFN value, which was calculated based on the 60-minute cumulative rainfall and SWI. RBFN output values ranged from 0 to 1.0, with a value closer to 0 indicating a larger rainfall magnitude and a value closer to 1.0 indicating a smaller rainfall.

Landslide disaster data
The disaster data used in this study were based on data collected by the Ministry of Land, Infrastructure, Transport and Tourism (MLIT) for the period 2003-2020 for all of Japan. The data was based on the reported date, place and cause of occurrence for each type of debris ow, slope failure and landslide reported by each prefecture. Among these three phenomena, "slope failure" corresponds to "debris avalanche" in the Hungr et al. (2014) classi cation, and "landslide" corresponds to "slide" and "spread". In this study, the names of the phenomena were used in the original data: debris ow, slope failure, and landslide.
In addition, this study addresses two types of landslides: debris ow and slope failures, which are covered by the Japanese LEWS, and landslides for reference.
Disasters caused by factors other than rainfall, such as earthquakes and snowmelt runoff, were excluded and limited to those caused only by rainfall. In addition, disasters for which the date of occurrence was not clear were excluded. In cases where the date of occurrence of landslides was known but the time of occurrence was not, the time was assigned to evaluate the maximum time the two axes of SWI and 60minute cumulative rainfall comprehensively were the peak of the rainfall.
In this study, landslides occurring on a smaller scale than those covered by Japanese LEWS are also included to understand the characteristics of landslides occurring in small-scale rainfall due to the in uence of antecedent rainfall and the actual situation of landslides occurring in nonexceedance critical rainfall events that have not yet been clari ed. (Unlike the disasters used for critical line setting, sporadic landslides that do not occur in a concentrated time and space were also covered.

Rainfall data
The rainfall-related indices were the 60-minute cumulative rainfall combined meteorological radar and ground rain gauges (Shinpo 2001), SWI, and their RBFN values. The basic characteristics were organized on one-hour intervals from June 2003 to September 2020 for each of the 223,186 grids, which will be discussed later. A series of rainfall events was de ned as a rainfall event with an RBFN value of 0.99 or less to exclude extremely small rainfall events and from the start of the event to 24 hours after the end of the event or 24 hours after the event fell below critical rainfall, whichever was later, as shown in Fig. 2 To analyze whether there is a difference in the relationship between disaster occurrence, rainfall exceedance, and nonexceedance of critical rainfall, the geology of each 1-km grid re ecting latitude and longitude (in Japan, this is called "National Land Numerical Information Tertiary Mesh") was classi ed using nine geological categories based on geological age (prehistoric, tertiary, and quaternary) and origin (sedimentary, volcanic, and plutonic rock/metamorphic rock), referring to the geological classi cation of Uchida et al. (2016). The rate of the number of rainfall events not exceeding the critical rainfall to the number of rainfall events was calculated for each geological classi cation. The geological classi cation of each grid was based on the AIST Geological Map of Japan (1:200,000) National Institute of Advanced Industrial Science and Technology (AIST) (2019), and the geological feature with the largest area occupied within a grid was treated as the geological feature of that grid.

Characteristics inventory
The procedure for linking rainfall index data and landslide data to classify rainfall is shown in Fig. 3.
Speci cally, the number of rainfall events and the number of disasters were calculated from the following two perspectives: pre/postrainfall period, exceeding/nonexceeding critical rainfall (15,151 events for debris ow and slope failures and 1,213 events for landslides).
In this study, the aforementioned method was used to cover the warm season (April 1~October 31) period from June 2003 to September 2020. In addition, because disaster data was based on reports from local governments and there was a large amount of data on disasters in populated areas. There were almost no data on disasters in unpopulated areas, areas without houses, plains (less than inclination 2 degrees), and water areas which were excluded from the object, in addition to areas where no critical rainfall was set. As a result, a database combining rainfall data, disaster data, and geological classi cation data for each 1-km grid was created for 223,186 grides out of 430,054 meshes nationwide excluding these areas.
The items in the database are shown in Table 1.
For the calculation of the unknown time data, when the date of occurrence of the disaster was a day with rainfall, it was counted as the minimum RBFN output value timing during rainfall. If the occurrence day was the day after rainfall or the day after falling below the critical rainfall fall, the data was counted as the RBFN minimum time during the immediately preceding rainfall event. If the date of occurrence was two days after the rainfall event or the day after falling below the critical rainfall fall, the data was not counted. The relationship between the time of occurrence of a disaster and the exceedance of the critical rainfall during rainfall was classi ed according to the timing of the occurrence of the event: pre, during, post, and after the end of the rainfall and the nonrainfall period. The number of rainfall events and the number of disasters occurring during a rainfall event were counted as the number of rainfall events (even if more than one disaster occurs within a 1 km grid in a rainfall event), while the number of disasters occurring after a rainfall event was counted as the number of disasters. The classi cation of the number of rainfall events and their details are shown in Fig. 4 and Table 2. 3.5. Retrospective rainfall data To understand the effect of antecedent rainfall on landslide nonexceedance critical rainfall, antecedent rainfall was determined retroactively from the date of occurrence of the disaster. The period for retrieving the antecedent rainfall and the rainfall characteristics to be extracted are shown in Table 3. During the disaster occurrence rainfall event period, the maximum 60-minute cumulative rainfall, the maximum SWI, and the minimum RBFN output values were determined. The time difference between the maximum 60minute cumulative rainfall and SWI and the time of the disaster event, in addition to the difference between exceeding and falling below the critical rainfall, were also determined for the periods of 28 days and 365 days before the disaster event, respectively. In the case of the search up to 28 days ago and 365 days ago, the rainfall periods including the date of occurrence of the disaster were excluded from the search. In the case of multiple landslides occurring in one rainfall event in a grid, the date and time of the rst occurrence was used as the representative.

Operational evaluation of LEWS in Japan
The accuracy of the estimation of landslide occurrence was con rmed based on inventory and rainfall data during the warm season from June 2003 to September 2020 for debris ow and slope failures, which were the targets of LEWS in Japan. To evaluate the accuracy of the LEWS in Japan, the recall value was calculated as the precision evaluation for occurrence and the speci city as the precision evaluation for nonoccurrence. These values were calculated based on the confusion matrix of the predicted and actual numbers shown in Table 4. Exceeding the critical rainfall that deals with rainfall that was predicted to occur on landslides, nonexceeding critical rainfall deals with rainfall that was not predicted to occur on landslides.
Exceeding rainfall, i.e., was predicted to produce landslides and did, was classi ed as true positive (TP), and rainfall that did not produce was classi ed as false-positive (FP), type-I error. Nonexceeding rainfall, i.e., was predicted to not occur on landslides and did not, those that did occur were classi ed as true negative (TN), and those that did occur were classi ed as false negative (FN) type-II errors.
Recall is the percentage of correct answers among the actual "occurrences" in the confusion matrix, as shown in Equation (1). Additionally, the speci city in Equation (2) indicates the likelihood of making a correct answer for a nonoccurrence.  Figure 5 shows the number of disasters for debris ows, slope failures and landslides during the pre/postrainfall period. In terms of the number of disasters that occurred during the pre/postrainfall period, 19.3% of the 15,151 cases of debris ow and slope failure and 27.6% of the 1,213 cases of landslides occurred. Landslides, which were considered to be affected by deep groundwater levels, occurred more than 8% during the pre/postrainfall period.

Number of rainfall and events
Tables 5-8 show the results of each case in Table 2, debris ow, slope failure, and landslide, respectively, during the pre/postrainfall period. The unit of the number in the table for the rainfall is the number of rainfall events, and the unit of the number for the pre/postrainfall is the number of events.
The number of debris ows and slope failures in Table 5 is almost the same as the number of rainfall events, with 4,904 rainfall events exceeding critical rainfall and 5,182 rainfall events not exceeding critical rainfall. However, there was a large difference in the number of nonexceeding rainfall events, with 419,894 exceeding the critical rainfall amount and 5,992,232 nonexceeding critical rainfall. The occurrence rate of all events in exceeding critical rainfall based on rainfall events was 4,904/424,888 = 1.15%. In contrast, the nonexceeding critical rainfall rate was 5,182/5,997,414 = 0.09%, a difference of more than 10 times. For the pre/postrrainfall disaster period, nonexceeding rainfall events are by far the most common (Table 6).
For landslides, as shown in Tables 7 and 8, the number of disasters was less than 1/10 of the number of debris ows and slope failures, but the ratio of exceeding rainfall to nonexceeding rainfall was similar, indicating the same trend. The trend in the number of disasters occurring pre/postrainfall periods was similar, with the number of disasters occurring in nonexceeding rainfall events being far greater than those occurring in exceeding rainfall events.
Although the occurrence rate based on the number of rainfall events was more than 10 times greater for exceeding rainfall events than for nonexceeding critical rainfall events, the fact that occurrence in nonexceeding rainfall events was not infrequent suggests that it is important to examine the impact of retrospective rainfall events.

Relationship between geology, number of events, and critical rainfall
To analyze the relationship between disaster occurrence, geological classi cation, and exceeding/nonexceeding critical rainfall, the ratio of the number of rainfalls in exceeding/nonexceeding critical rainfalls to the number of rainfalls in two cases, debris frow, slope failure, and landslide, was determined for each geological classi cation using nine geological classi cations based on geological age and causes by each 1-km grid. "Slope failure" here refers to "debris avalanche" in Hungr's et al. (2014) Loading [MathJax]/jax/output/CommonHTML/jax.js classi cation, while "landslide" corresponds to "slide" and "spread". The ratio of the number of rainfall events exceeding/not exceeding the critical rainfall for debris ow and slope failure and the compositional ratio of each geological category are shown in Fig. 6(a)-(d) show those for landslides.
For debris ow and slope failure, the highest percentage of rainfall occurrence was in the Quaternary sedimentary rocks. Although the plains are excluded from the target grid of this study, because the disaster data was based on disaster reporting, the most common geology in the compositional rate was still Quaternary sedimentary rock, which accounts for approximately 1/4 of the total. This may also be because the area has a large population exposed to hazards close to urban areas such as terrace cliffs and hillsides. For sedimentary and volcanic rocks, the disaster occurrence rate increases with increasing geological age, regardless of whether the critical rainfall is exceeded, which may indicate the degree of solidi cation in the case of sedimentary rocks and the susceptibility to disasters in the volcanic ash layer in the case of volcanic rocks. Although the compositional rate of tertiary geological units in metamorphic rocks and Paleozoic rocks was small, the disaster occurrence rainfall rate was above the average because it does not exceed the critical rainfall, indicating that the geology was prone to disasters.
For landslides, unlike debris ows and slope failures, a larger-than-average rate of occurrence rainfall rate occurred in Tertiary sedimentary rocks and in Plutonic rocks and Metamorphic rocks of the Mesozoic/Paleozoic Era, which is consistent with the fact that landslides are more common in these geological regions. respectively, and the number and percentage of exceeding critical rainfall for each category. In addition, Table 9 shows the statistical data of these rainfall indicators. Distribution of these rain indices maximum value of debris ow and slope failure, and landslides were all highly variable, the number of rainfall occurrences was higher in the categories of 20-40 mm/60 min for maximum 60-minute cumulative rainfall, 100-200 mm for maximum SWI, and 0.9 or higher for minimum RBFN output value. However, these were the nonexceeding critical rainfall events, and therefore, these indices were not very large. Additionally, as shown in Table 9, there is little difference in the statistical characteristics of those rainfall indices for the 28-day and 365-day periods. For debris ow and slope failure, landslides with nonexceeding critical rainfall, the maximum 60-minute cumulative rainfall and SWI, minimum RBFN output value and the rate of exceeding critical rainfall (number of exceeding critical rainfall/number of total rainfalls) for the period of 28 days back from the date of disaster occurrence, excluding the disaster of rainfall period, were searched. In addition, the timing of those maximum or minimum rainfall indices was also investigated. In the case of debris ow and slope failure, 100% of the cases exceeded critical rainfall one or two days before, but only a small percentage of the cases experienced rainfall exceeding critical rainfall three days to four weeks before, which means that the critical rainfall a few days before was the one that should be considered in the previous period. In addition, due to the small number of cases, it was not possible to ascertain the rainfall indices that should be considered in the previous rainfall period, since only a few cases had both large 60-minute cumulative rainfall and SWI. However, in the case of landslides, it should be noted that there are many rainfalls of such a scale that critical rainfalls were exceeded in the period from 7 days to 2 weeks prior to the event. As a result of examining the effects of antecedent rainfall retrospectively up to the 28th, it should be noted that debris ow and slope failure were more likely to occur with nonexceeding critical rainfall if there was signi cant rainfall that exceeded critical rainfall by approximately two days and landslides by one to two weeks prior to the event.

Effect of antecedent rainfall
For the results of the 365-day retrospective analysis, as shown in Fig. 11, there were no large peaks in the exceeding critical rainfall rate, and the number of exceeding critical rainfall events was large 40 weeks ago, but this was due to the rainfall period of the previous year, and in effect, the in uence of rainfall prior to 28 days was considered to be negligible.
In the case of landslides, as in the case of debris ow and slope failure, there was no signi cant exceeding critical rainfall for the period prior to one or two weeks, and the exceeding critical rainfall 40 weeks prior was considered to be due to the rainfall of the previous year. Table 10 shows the operational results in Japan based on the number of rainfall events and disasters in exceeding/not exceeding critical rainfall for debris ows and slope failure from June 2003 to September 2020, including landslides caused by small rainfall events. The recall as the occurrence accuracy of LEWS was 0.486, which was not so high, yet the speci city for the nonoccurrence accuracy of LEWS as 0.935, which means that LEWS can correctly predict the nonoccurrence of LEWS. However, these results were related to the probability of a landslide occurring as extremely low even under rainfall conditions that have the potential to cause a landslide, and it was considered realistic to evaluate the operational performance of the LEWS on a 1-km grid basis in terms of recall.

LEWS performance evaluation and geological characteristics
The analysis of the critical rainfall based on the rainfall events con rms that it was a "transition line". The separability of the so-called "threshold" was evaluated by the event occurrence rate around this in ection, regardless of the number of dimensions. Since the magni cation of rainfall as an incentive was 15 times higher than the critical rainfall, the incentive was interpreted as an ampli cation of the occurrence potential of the predisposing factor on the corresponding grid, and the knowledge on the applied geological predisposition can be integrated more effectively by superimposing the judgment for disaster prevention.
Since the multiplier for rainfall as an incentive was 15 times the critical rainfall, the incentive was interpreted as an ampli cation of the occurrence potential of the primary factor on the corresponding grid. By superimposing disaster response decisions, knowledge about primary factors in terms of geological predisposition can be integrated more effectively.
A coupled analysis of the relationship between disaster occurrence and geology and rainfall occurrence showed that, re ecting the geological composition and population distribution of Japan, inventories of debris ows and slope failures were more common in Quaternary sedimentary rocks, and the disaster occurrence rate was higher in sedimentary rocks and volcanic rocks with a more recent geological age.
Compared to the Quaternary sedimentary rocks, the relatively Plutonic and Metamorphic rocks had more failure cases (false negative) in nonexceeding critical rainfall, which posed an issue for LEWS. It was also con rmed that the geological view of landslide occurrence re ected the distribution of event occurrence.

Antecedent rainfall for LEWS
Due to its high suitability across the country, Japan has adopted a frequency-based approach to criteria development that combines short-term and long-term rainfall indices and learns from a database of past long-term rainfall. Although the method re ects such a large amount of technological accumulation, approximately half of the disaster events do not exceed critical rainfall, and furthermore, almost 10-30% of the events are outside of rainfall events. As a result, it was con rmed that the fast-moving debris ow and slope failures had a certain amount of rainfall one to two days before the rainfall period, and the relatively slow-moving landslides (slide, slip, spread) had a certain amount of rainfall of one to two weeks during the 28-day period. In the case of re ecting the residual moisture in the ground for such a long period of time, slope hydrological experience shows that simply reducing the diminishing rate of the antecedent rainfall index as in the past may signi cantly increase the false alarm (false-positive), which may greatly affect the practical reliability of LEWS. For example, this problem cannot be avoided by using the hydrological indices and processing methods of Hong Kong (24-hour total rainfall), which operates a Loading [MathJax]/jax/output/CommonHTML/jax.js comparable LEWS, or other countries that use 2-4 days of total rainfall and its probability value. Therefore, rather than improving the hydrological model, it would be more effective to consider a method to appropriately learn the rainfall history during the affected period as an operational rule to reduce the negative impact of reducing the effectiveness of LEWS. In addition, since the search was conducted 52 weeks previous in this study, it could be concluded from the data handled that there was no need to consider the warm season history of one year ago. Limiting the period of time considered in past rainfall history to approximately 28 days was very signi cant for the development and operation of LEWSs.

Quality of inventory and future subject
In this analysis, the occurrence rate was calculated by incentive factors alone because a series judgment system was adopted that does not include both primary factors and incentive factors at the same time. In addition, because of the operational indicators and critical rainfall, the evaluation relied on rainfall data available in Japan and inventories.
Geology was represented as a factor affecting the risk of the primary factors by the AIST geology data of approximately 1 km 2 . The appropriateness of re ecting detailed local geology in grid-scale assessments needs to be re-examined in the future. Additionally, how to make the topographic factor representative at 1 km 2 could be an applied geomorphology issue.
It cannot be denied that the evaluation of this study was affected by changes in data quality over time due to the improvement of the analysis scheme for radar AMeDAS analytical rainfall, the scale of each year and disaster event, and the reliability of various reports from different prefectures.
There is room for the unique reporting of landslide categories in Japan and improvement in the use of remote sensing in the future, as it could not cover the cases of disasters that occurred in the backcountry without people knowing. In addition, the majority of landslides in snow-covered cold regions occur during the snowmelt season, so it is necessary to consider the "cold weather" period in the future.

Conclusions
A coupled analysis of the relationship between disaster occurrence and geology and rainfall occurrence showed that the geological characteristics of Japan, especially the distribution of disaster events, were remarkable and that the rainfall history of LEWS was affected by this distribution.
In this study, based on 17 years of analytical rainfall and soil rainfall index data from 2003 to 2020 and disaster data based on disaster reports, in/out of the series of rainfall, the number of disaster occurrences/number of disaster occurrence rainfalls in exceeding/nonexceeding critical rainfall, and the occurrence rainfall rate by geology were con rmed in a 1-km grid unit.
A total of 19.3% of the total number of debris ows and slope failures and 27.6% of the total number of landslides were disasters of the pre/postrainfall period. In the case of debris ow and slope failures, the number of occurrence rainfalls exceeding/not exceeding critical rainfall were almost the same, yet the Loading [MathJax]/jax/output/CommonHTML/jax.js occurrence rate was more than 10 times higher when the rainfall was exceeding. The occurrence rate for rainfall exceeding the critical rainfall based on the number of rainfall events was 1.15%, while the occurrence rate for nonexceeding rainfall was 0.09%, a difference of more than 10 times.
The geology with the highest occurrence rate of debris ow and slope failure was Quaternary sedimentary rocks, and the occurrence rate of sedimentary and volcanic rocks increased with age. In terms of landslides, the occurrence rate in Tertiary sedimentary rocks and in Plutonic rocks and Metamorphic rocks of the Mesozoic/Paleozoic Era was higher than average, which was consistent with the characteristics of landslides in Japan.
Since there were many landslides that occurred in nonexceeding critical rainfall, and these may be affected by the antecedent rainfall, the maximum values of 60-minute cumulative rainfall, and SWI were con rmed back to 28 days and 365 days. In the case of debris ow and slope failures, the exceedance rate was 100% when the critical rainfall was exceeded one or two days ago, and it was determined that the critical rainfall a few days ago was the previous period's rainfall that should be considered. In the case of landslides, landslides were more likely to experience nonexceeding critical rainfall if there was a large amount of rainfall that exceeds rainfall within the period of one to two weeks before the landslide.
For the operational evaluation of the critical rainfall, in the case of debris ow and slope failure, which are the subject of the LEWS in Japan, the recall for the occurrence was 0.486, which was related to the fact that almost half of the cases occur in nonexceeding critical rainfall. The speci city as the accuracy for nonoccurrence was 0.935, which was affected by the nonoccurrence of nonexceedance rainfall data (true negative) that account for most of the data. For the operational performance of the LEWS, it was considered realistic to evaluate it on the basis of recall.
Operational evaluation of LEWSs as disaster warnings has been performed for signi cant disaster cases and at the regional level. However, there has been no long-term analysis of actual disasters on a national scale with high resolution in both time and space. The comprehensive evaluation in this study clari ed issues in LEWS evaluation that could not be con rmed in case studies and regional-level evaluations.
Even with the critical rainfall based on short-term and long-term rainfall indices (antecedent rainfall indices) optimized for the occurrence rainfall, the number of occurrence rainfall events corresponding to nonexceeding critical rainfall events accounts for half of the total number of occurrence rainfall events.
There were data limitations in discriminating between occurrence and nonoccurrence based on rainfall observations alone (errors in hypothesis testing (i.e., striking out to predict "occurrence" even though the event has not occurred (false-positive), type I error), missing the event even though it has occurred (false negative), type II error), and setting the optimal threshold between the two). Therefore, to ensure LEWS, it was essential to cascade regional observations and local monitoring of individual locations, in addition to monitoring with national rainfall indicators.
In Japan, there is room for a multilayered decision-making system to re ect antecedent rainfall approximately one or two days earlier than the single rainfall period. Even now, simple resetting of Loading [MathJax]/jax/output/CommonHTML/jax.js antecedent rainfall by using a highly continuous rainfall index (SWI) is avoided, and weaknesses that effectively return to near initial values after a certain no rainfall period are the same as the weakness of the simple integrated rainfall method and the effective rainfall method. In the case of landslides (sliding or spreading), it is also necessary to add a decision method that considers rainfall history over a period of 7 days to 2 weeks. However, practically no effect of the rainfall history prior to the 28th was con rmed. Therefore, it is not necessary to include the effects of the previous year's heavy rains, for example. To develop and select long-term rainfall indices, it is su cient to include a history of 28 days or less.

Declarations Funding
We have not received any nancial support for this research. Tables   Table 1. Description of the sediment disaster database.  Table 3. Time required to extract historical rainfall and rainfall index data using the maximum rainfall index. Table 4. De nition of confusion matrix.  Table 6. Numbers of debris ow events and slope failures that occurred during the pre/postrainfall period. Table 7. Numbers of rainfall landslides that occurred during rainfall events. Table 8. Numbers of landslide events that occurred during the pre/postrainfall period. Three-dimensional RBFN output response surface based on 60-minute cumulative rainfall and SWI (soil water index) (left) and an example of a two-dimensional critical rainfall based on the response surface