*2.3. Inventory Methodology*

The formula of the E–D rainfall threshold is expressed as follow:

$$E = aD^{\mathcal{V}} \tag{1}$$

where *D* is the duration (unit: h) from the beginning of the rainfall (*Ts*) to the occurrence time of the landslide (*Te*), *E* is the accumulated rainfall (unit: mm) during this duration, α and γ are constant parameters calculated by the regression method. *Te* means the time when the landslide event occurred; but for the landslide event with a temporal resolution of the day at S3, *Te* is the time when the rainfall ended on that day, and *Ts* is the time when the rainfall event began. A rainfall event is defined by a no-rainfall period. Saito et al. (2010) used 24 h to define the rainfall event in Japan [24]; Brunetti et al. (2010) used 48 h in May–September, and 96 h in October–April in Italy [37]; Segoni et al. (2014) did several runs using different no rain periods to get the lowest number of false alarms; the no rain period varies 18–36 h for different alert zones [22]. In this study, a rainfall event is defined as continuous rainfall separated from the preceding and the following events by a no-rainfall period of no less than 24 h.

Firstly, the rainfall information (E and D) relevant to landslides needs to be acquired. As CMORPH and merged rainfall data are both gridded data, the grid whose center is closest to the location of the landslide event is selected to reconstruct the rainfall information for landslides.

Then, Formula (1) is log-transformed to a linear equation:

$$
\log 10 \text{ (E)} = \log 10 \text{ (a)} + \gamma \log 10 \text{ (D)}\tag{2}
$$

For each landslide event, E–D values are plotted on the log10-log10 graph. In this process, it has been found that the rainfall durations of some landslide events are 0 h, which may be due to the fact that part of the landslides are not triggered by short-term rainfall, but by earthquake, snow melt or antecedent rainfall. Moreover, the AWSs coverage is not wide enough in China, especially in the mountain areas, therefore, such landslides are excluded when calculating rainfall thresholds. Finally, based on the CMORPH products, 367 landslides are selected to calculate the rainfall thresholds; based on the merged rainfall products (available from 2008), 276 landslides are used to construct the rainfall thresholds.

To calculate the rainfall thresholds for landslides, the quantile regression [38] is adopted to determine the rainfall E–D threshold in this study. R software has a package called "quantreg", which implements the quantile regression [39,40]. It has been proposed that different levels of early warning information can be issued by the EWS with probability levels of 5%, 20% and 50%, categorized as "Null" (below the 5th percentile), "Alert" (5–20th percentiles), "Warning" (20–50th percentiles) and "Evacuation" (above the 50th percentiles), respectively. In this paper, the 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th and 90th percentile values are calculated for quantile regression lines at different levels, and the values of intercept α and slope β are returned by the linear regression method.

The main procedures for calculating the thresholds are summarized as follows.


In addition, China is affected by the monsoon system. With the onset of the summer monsoon in May, the mainland of China becomes wet and rainy from south to north. When it comes to September, the summer monsoon retreats rapidly, followed by the establishment of the winter monsoon, and then the mainland of China is controlled by the Siberia high in winter. During this period, the soil is dry due to less rain. Considering the special climate conditions in China, the rainfall characteristics and soil moisture are different between the two periods in each year. Thus, the periods of May–September and October–April are selected as the rainy season and non-rainy season, respectively [41]. Moreover, as mentioned in Section 1, the existing landslide warning system shows different warning effects in rainy and non-rainy seasons [11], so the rainfall thresholds for the rainy and non-rainy seasons are calculated respectively in this paper.

#### **3. Results**

By using the landslide events occurred during 1998–2015 in China which satisfy the requirements mentioned above, that is, the spatial resolution at the levels of county, district or higher, and the temporal resolution at the level of day or finer, the D and E for each landslide event are inferred from the merged and CMOPRH rainfall data.

Figure 3 shows the distribution of the rainfall conditions for each landslide event in the log10-log10 graph. Roughly taking 48 h as a split point, the trend seems different in the two parts, which can be seen in both the CMORPH and merged rainfall data during the rainy season and non-rainy season. Thus, the duration can be divided into two periods: short duration (1 ≤ D < 48 h) and long duration (D > 48). This may be because the mechanisms of landslide and debris flow triggered by long-term rainfall and short-term rainfall are different. In the long-term rainfall, the threshold is affected by the antecedent precipitation and soil moisture, and the evaporation is also an important factor [25]. In Figure 3a, for the merged data, in the rainy season, the range of the accumulated rainfall is 1.02–388.68 mm and the duration is 1–412 h (around 17 days); in the non-rainy season (Figure 3b), the range of the accumulated rainfall is 1.04–271.39 mm and the duration is 2–291 h (around 12 days). For the CMORPH data, in the rainy season (Figure 3c), the range of the accumulated rainfall is 1–394.8 mm and the duration is 1–341 h (around 14 days); in the non-rainy season (Figure 3d), the range of the accumulated rainfall is 1.2–179.4 mm and the duration is 1–393 h (around 16 days).

**Figure 3.** Event–duration (E–D) conditions of landslides calculated by the merged rainfall in the (**a**) rainy season and (**b**) non-rainy season, and by the Climate Prediction Center Morphing (CMORPH) rainfall in the (**c**) rainy season and (**d**) non-rainy season with different quantile regression lines (5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and 90% from bottom to top).

The coefficients of intercept α and slope γ at different levels of quantile regression lines obtained by combining precipitation and CMORPH precipitation are listed in Table 2. By using thresholds at different levels of quantile regression, different levels of warnings can be established in the EWS [42]. Generally, the threshold at the 5% quantile level is used as a lower safety threshold. If the threshold exceeds the value at the 5% quantile level, relevant tracking, monitoring and prediction should be carried out; if the threshold exceeds the value at the 20% quantile level, attention should be paid; and if the threshold exceeds the value at the 50% quantile level, people should be evacuated.

It can be found that for the thresholds at the quantile level of 50% or below, the slope of the regression line for the thresholds in the events with long durations is bigger than those with short durations, which means for long duration events much more rainfall is required to trigger landslide than. The possible reason might be that the evaporation plays an important role in the events with long durations, while for those with short durations, the evaporation can be ignored. Furthermore, the antecedent precipitation, soil moisture and climate condition also influence the rainfall thresholds in the initiation of landslides, and we will discuss this later in this article.


**Table 2.** Coefficients of intercept α and slope γ at different levels of quantile regression lines obtained by combining precipitation and CMORPH precipitation.

Considering that the MAP varies greatly in China (Figure 2), the accumulated rainfall is normalized by MAP. Figure 4 shows the scatter diagram of the relationship between EMAP and D on the logarithmic coordinates and the quantile regression lines at different levels. In addition, the corresponding coefficients of slope γ and intercept α for quantile regression lines at different levels are shown in Table 3. Similar to the E–D formula, split by 48 h, the formulas for both short-term and long-term rainfall thresholds are established, respectively. It can be seen that for the EMAP–D thresholds at the 50% quantile level or below established by the merged and CMORPH rainfall products, the slope of the regression line on rainfall threshold for the landslide and debris flow triggered by short-term rainfall is generally smaller than or close to that triggered by long-term rainfall, while the intercept is higher than that triggered by the long-term rainfall. The difference in the mechanisms for landslide and debris flow triggered by long-term rainfall and short-term rainfall is reflected in the rainfall thresholds.

**Table 3.** Same as Table 2, but for the coefficients of EMAP–D thresholds. (EMAP–D: E–D thresholds normalized by mean annual precipitation).


**Figure 4.** Same as Figure 3, but for normalized E–D thresholds (EMAP–D).
