**4. Discussions**

So far, four groups of rainfall thresholds in China have been established. Each group consists of four sub-thresholds in rainy season and non-rainy season (both are divided into short duration and long duration), respectively. For thresholds below the quantile level of 50% derived from both the merged and CMORPH rainfall products, the slope of the regression line of the rainfall threshold for long durations is higher than that for short durations, which may be attributed to different mechanisms in triggering landslides by long- and short-duration rainfall.

In our previous study, a statistical model for landslide has been established by using the landslide susceptibility and a global rainfall threshold, showing that around 70% of the landslide events occurred in China during 2016–2017 can be warned in advance by the model [11,12]. In addition, when the rainfall threshold exceeds the value at the quantile level of 20%, attention should be paid. Therefore, the rainfall threshold at the quantile level of 30% is compared to other existing thresholds, and it is validated by using the landslides occurred in 2016–2017. Finally, the warning ability is compared with the previous statistical model for landslide.

The E–D thresholds with other global and regional thresholds in the literature are listed in Table 3. The I–D rainfall thresholds are converted to the E–D thresholds, and then all these thresholds are plotted on the log10-log10 graph (Figure 5). For the long duration, the thresholds derived from both the merged and CMORPH rainfall products are higher in the rainy season than those in the non-rainy season. For the short duration, the thresholds derived from the merged rainfall product are higher in the rainy season than those in the non-rainy season, but the thresholds from the CMORPH rainfall product in the rainy season are similar to those in the non-rainy season.

It can be seen that the thresholds established in this study are lower than most of the thresholds in previous studies shown here, especially for the short duration, including the global thresholds [43–45], the regional thresholds in Puerto Rico [46], Taiwan as well as Zhejiang of China [47,48]. This provides important information for the early warning of landslides in China, that is, the landslides occurred in China might be triggered by lower rainfall thresholds than that recognized before, which might result in missing alarms. The long-duration thresholds established in this study are close to the global thresholds defined by Guzzetti et al. (2008) (the line indicated by number 3-2 in Figure 5) [25] and the regional thresholds for Yan'an in China (the line indicated by number 10 in Figure 5) defined by Chen and Wang (2014) [49]. In addition, Li et al. (2017) defined a rainfall threshold (the line indicated by number 6 in Figure 5) for the whole China with 60 landslide events occurred in June to September during 2005–2011. This threshold is higher than the threshold defined in this study in the rainy season (May to September) [15]. It might because more landslide events (60 versus 660 events) were used in this study to obtain the warning thresholds.

**Figure 5.** Comparison between E–D thresholds defined in this work and previous published thresholds. The numbers refer to No. in Table 4.

The EMAP–D thresholds are also compared with other thresholds defined in previous studies, as listed in Table 5, and these thresholds are plotted in Figure 6. The thresholds in rainy season calculated by using merged and CMORPH rainfall products are all higher than those in the non-rainy season. For short duration, the thresholds in this study are close to the thresholds calculated by Guzzetti et al. (2008) [25], higher than the Japan threshold established by Saito et al. (2010) [24]. For the long duration, the thresholds are higher than or very close to the thresholds calculated by Guzzetti et al. (2008) and Saito et al. (2010) [24,25].


**Table 4.** Rainfall thresholds for landslide occurrence in this work compared with those in previous publications.



**Figure 6.** Comparison between the EMAP–D thresholds defined in this study and previous published thresholds. The numbers refer to No. in Table 4.

The comparison with other thresholds indicates that the landslides in China can be triggered by less severe rainfall conditions than previously recognized, which provides important information for the assessment of landslide hazards. In other words, China is highly prone to landslides compared with most other regions in the world. This may be caused by the large areas of mountains and hills, the monsoon climate and active human activities (constructions) of China.

The rainfall thresholds are validated by the 106 landslide and debris flow events occurred during 2016–2017, and the rates of these events, which can be warned in advance by the thresholds in this paper or the original landslide model developed by Wang et al. (2016), is called a "positive rate" here [11]. As shown in Figure 7, it can be seen that the positive rate of the original statistical model for the landslide events in 2016–2017 is 66%, and that of the rainfall thresholds established in this paper is 80–86%. In the rainy season, the positive rate of the original model is 72%, while that of the improved rainfall thresholds is 82%–89%. In the non-rainy season, the positive rate of the original model is only 35%, while that of the improved rainfall thresholds reaches 55%–73%. The positive rates in the whole year, the rainy season and the non-rainy season have increased by 16%–20%, 10%–17% and 20%–38%, respectively. Thus, if these thresholds can be applied in the EWS, more landslides can be warned in advance.

**Figure 7.** Comparison of positive rates between the improved thresholds and those in the original model [11].

Moreover, the "positive rate" is significantly improved if the thresholds in this study are adopted, however, a higher positive rate does not mean the threshold is better, because higher "positive rate" usually means the false alarm might also be higher, thus in real world application, the threshold defined in this paper should be carefully tested in real-time warning application. Actually, it's impossible to calculate the false alarms because the landslide inventory collected in this study is incomplete. Although the number of events in the catalog is much more than that in previous studies, it's still far from enough. For instance, according to the National Geological Disaster Bulletin, there is an average of 12,126 landslides per year during 2007–2016, but only a total of 771 events in 1998–2017 are collected through reports and the news online. So the false alarms would be inaccurate even if the calculation is conducted on them, which is one of the limitations in this study. In the future work, a more complete dataset of landslides and debris flows will be collected to find the most suitable rainfall thresholds for the warning of landslides and debris flows in the regression threshold lines at different quantile levels.

Furthermore, the differences between thresholds in different durations and seasons suggest that soil moisture plays an important role in the rainfall conditions triggering the landslides, and thus the antecedent rainfall is also important for landslides triggered by long-duration rainfall events. A detailed analysis of these factors, which is related to the physical process of landslide dynamic, is not provided in this study. The rainfall thresholds represent an empirical relationship between the landslides and rainfall that is generally similar to the parameterization of cloud processes in the weather model. Thus, it is still effective for the early warning of landslides. The uncertainty of forecasted precipitation in weather models has an important impact on the early warning of landslides. Recently, the ensemble forecast has been developed to cope with this uncertainty in weather models, which provides a new train of thought for the early warning of landslides. In further studies, based on the rainfall thresholds in this study and others, a landslide ensemble forecasting system (LEFS) is expected to be established to improve the prediction for landslides.

## **5. Conclusions**

In this study, based on the landslide events occurred in China during 1998–2017, four groups of rainfall thresholds for landslide occurrence are defined by using the regression values at different quantile levels of the quantile regression. Based on both the merged rainfall product and the CMORH rainfall product, two kinds of rainfall thresholds—the cumulated event rainfall-rainfall duration thresholds (E–D) and the thresholds normalized by MAP (EMAP–D) are established respectively. Each group consists of four sub-thresholds in rainy season and non-rainy season (both are divided into short duration and long duration).

The slope of thresholds in the events with long durations is higher than that with short durations for thresholds below the quantile level of 50%, which may be due to different mechanisms of landslides triggered by long duration rainfall and short duration rainfall. The evaporation and antecedent rainfall become more important for landslides triggered by long duration rainfall events. Besides, the rainfall thresholds in the non-rainy season are generally lower than those in the rainy season.

The thresholds defined in this study are compared with those in previous studies. The E–D thresholds in this study are generally lower than most of the other thresholds, including the global thresholds, the regional and national thresholds in China, which may be because more landslide events in China were used in this study. Moreover, it also suggests that the combined effects of special geological environment, topographical relief and climate conditions make China suffer landslides more frequently and severely than other regions in the world. The landslide events occurred in 2016–2017 are used to validate the rainfall thresholds. Compared with the previous statistical model for landslides, based on the improved rainfall thresholds, the positive rates for the landslide and debris flow events have increased by 16%–20%, 10%–17% and 20%–38% in the whole year, rainy season and non-rainy season, respectively.

This paper aims to establish rainfall thresholds for its application in landside early warning systems. In addition to the triggering factors, the geological environment is also important, which decides the landslide susceptibility in a specific region. Thus, combining multiple rainfall thresholds with the landslide susceptibility map, and by using the real-time rainfall produced by CMORPH (CMORPH-RAW) and the forecasted rainfall from ensemble numerical weather prediction models, the LEFS will be established in future work. We expect it will contribute to saving lives and mitigating property damages caused by landslide disasters.

**Author Contributions:** Conceptualization, J.W.; methodology, J.W. and S.H.; software, J.W. and S.H.; validation, S.H. and S.L.; formal analysis, S.H.; investigation, S.H.; resources, J.W.; data curation, S.H.; writing—original draft preparation, S.H.; writing—review and editing, J.W.; visualization, S.H. and S.L.; supervision, J.W.; project administration, J.W.; funding acquisition, J.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Key Research and Development Program of China (Grant No. 2016YFA0600703) and the National Natural Science Foundation of China (Grant No.41605084).

**Acknowledgments:** We thank Wu Jia and Gao Xuejie for providing CN05.1 data. And we acknowledge the NOAA CPC for providing the CMORPH data and the Conservation Science Program of World Wildlife Fund for providing DEM. We thank Nanjing Hurricane Translation for reviewing the English language quality of this paper.

**Conflicts of Interest:** The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
