The debris flows mentioned in this study limit to the torrential flow of a mixture of water, mud, and debris in the gully or channel of a small catchment, even on a hill slope. The time span of the collected debris-flow events to the earthquakes does not exceed 15 years. Data of some debris-flow events when near-zero rainfall was recorded from a gridded rainfall dataset are excluded (more details in 2.2.2). Then, 267 debris-flow records for 2000–2010 in the WEA, 109 for 2000–2017 in the LEA, and 70 for 2010–2018 in JEA were collected through field survey and data gathering from Sichuan Provincial Natural Resources Department (Figure 1; Table 1). In the WEA, the debris flows that happened on the same day with the earthquake are classified as post-earthquake events, which can be used to show extremely post-seismic impacts on the rainfall conditions. Unlike debris flows in the WEA, we collected no co-seismic debris-flow records in the LEA and JEA.

The gridded near-surface meteorological dataset was developed for evaluating land surface processes in China (He et al., 2020). The dataset was made through the fusion of remote sensing products (e.g., Tropical Rainfall Measuring Mission 3B42 v7), a reanalysis dataset (e.g., Global Land Data Assimilation System and Modern-Era Retrospective Analysis), and in-situ observations at weather stations (e.g., daily data from approximately 700 stations of China Meteorological Administration and sub-daily data from the National Oceanic and Atmospheric Administration’s National Centers for Environmental Information). The time of the data ranges from January 1979 up to December 2018 with a temporal resolution of 3 h and a spatial resolution of 0.1°. For each 0.1° grid cell, a rainfall record with Greenwich Mean Time (GMT) stands for a mean value of rainfall intensities (mm/h) taken every three hours. So, each grid cell represents 8 records on each day. The data have been adjusted to match the Beijing time, i.e., 8 h ahead of the GMT.

Based on the data, the mean annual rainfall of 1979–2018 is ca. 950, 1,360, and 660 mm for the WEA, the LEA, and the JEA, respectively. According to the time ranges in Table 1, the mean annual rainfall of 937 mm after 2008 in the WEA is 7% higher than before 2008. However, the number of debris flows per year has increased ca. 30 times compared with the period before the Wenchuan earthquake. The decrease in the number of debris flows in both the LEA and the JEA cannot be directly linked with the change in the mean annual rainfall, suggesting that more short-term rainfall conditions should be discussed.

Effective rainfall is considered as a function of the regressive rainfall index (Li et al., 2011; Zhuang et al., 2015). We use the ratio of effective rainfall to annual rainfall as the dimensionless effective rainfall (DER) to eliminate the impacts of different annual climate. The equation for calculating DER can be written as: DER = ∑ i= 1 n K i P i + P 0 P annual (1) where P ₀ is the total rainfall on the day of debris-flow occurrence; P _i is the accumulative daily rainfall (mm) on the ith day before the occurrence; K ⁱ indicating K to the power of i is the decay factor of precipitation on the ith day before the occurrence; and P _annual is the total rainfall for each year. The study areas belong to the Hengduan Mountains in the southwest region of China, therefore, the K is empirically set to 0.84 (Liu et al., 2020). n is set to 3, 7, 11, and 15, respectively, for comparison. The median of DER in each earthquake-affected area is regarded as a proxy of regional rainfall threshold.

The so-called rainfall intensity-duration (I-D) relationship was proposed firstly by Caine (1980). It is a fairly common type of debris-flow threshold (Guzzetti et al., 2007). The original expression of the relationship is of discrepant dimension as the following: I = α D − β (2) where the term I denotes the mean hourly rainfall intensity (mm/h) of a continuous rainfall process that triggers a debris-flow event; D is the rainfall duration (h) for triggering a debris-flow event; and α and β are coefficients. Then, when the curve is drawn in a double logarithmic coordinate system, the α can reflect the intercept, while β can reflect the slope of the straight line. The rainfall conditions above the curve are more likely to trigger debris flows. Although some studies emphasize the physical interpretation of parameters in I-D curve, it is now restricted to some specific kind of debris flows such as runoff-generated debris flows with enough in-situ observations (Berti et al., 2020).

To eliminate the impacts of different annual climates before and after an earthquake, the ratio (I _new , h⁻¹) of mean hourly rainfall intensity (mm/h) to annual rainfall (mm) is used to replace the term I in the Eq. 2 as follows: I n e w = α n e w D − β n e w 2a where α _new and β _new are new coefficients. It is noteworthy that only the “day” information of debris-flow occurrence is available. It is assumed that a continue rainfall process begins if when averaged hourly rainfall intensity of grid cells covering the debris-flow gully is greater than 0.05 mm/h. Thus, the I _new and D of such rainfall event were used to describe the rainfall process for triggering debris flows.

The impact of each earthquake on the thresholds is determined by the following equation: Impact = ( Thr e pre − Thr e post ) Thr e pre × 100 % (3) where Thre _pre denotes the median DER or the parameters of I-D curve before the earthquake; and Thre _post indicates those after the earthquake. For the DER, the positive value of Impact indicates the decrease of the regional rainfall threshold. For the parameters of I-D curve, the positive impact on α indicates a decrease of the scaling constant after an earthquake, α _new of I _new at D = 1 in the power-law relationship indicates that post-earthquake rainfall intensity is smaller or greater than the pre-earthquake intensity. The positive impact on β _new indicates a decrease of the shape slope, which should be combined with α _new change for threshold analysis.

The impact of the Wenchuan earthquake is reported to be ca. 20–30% (Tang et al., 2009; Ma et al., 2017). Compared with these studies, debris-flow records from more timely and detailed investigations after earthquakes have been collected, especially for the Wenchuan earthquake, meaning more debris flows with smaller rainfall have been included for statistical analysis. In addition, we supplemented the data analysis on the Lushan earthquake in 2013 and the recent Jiuzhaigou earthquake in 2017, and further explored the impacts of the earthquake on regional rainfall threshold. The impacts of the Lushan and Jiuzhaigou earthquakes on I-D rainfall thresholds are smaller, which may be due to the fact that moderate magnitude earthquakes (Mw 6–7) produce less landslide-associated loose materials (Stoffel et al., 2014).

Lin et al. (2004) concludes that the triggering thresholds such as cumulative antecedent rainfall and hourly rainfall intensity significantly decreased by 33% after the Chi-Chi Earthquake compared to the values before the earthquake. Shieh et al. (2009) surveyed the Wushihkeng watershed and the Mt. Ninety-Nine watershed in the Chi-Chi earthquake area. The maximum effective cumulative rainfall threshold was about 50% of that before the earthquake. Similar outcomes can be found in the Chen-Yu-Lan watershed (Chen, 2011). The 30–50% change caused by the Chi-Chi earthquake is indeed similar to that by the Wenchuan earthquake.

As shown in Table 2, the moment magnitude of the Wenchuan earthquake reached 7.9, much higher than the others. Although the change in the median DER is close to that influenced by the Lushan earthquake, the α _new of the I-D curve in the WEA has been changed by 45%, which is nearly double in the LEA. With a similar moment magnitude, different focal depths affect the results. The change in the median DER in the LEA with a 13 km focal depth is 11% larger than the JEA with 20 km focal depth.

A warning strategy, including the DER and I-D curves can be considered by using similar settings of methods and data as in this study. The DER threshold should be the initial focus. The antecedent rainfall can be obtained from up-to-date meteorological data, such as near-real-time precipitation produced by the land data assimilation system (CLDAS) from the China Meteorological Data Service Center (http://data.cma.cn/), satellite data, and in-situ observation. The daily rainfall data is obtained from the weather forecast. When the earthquake magnitude is ca. 6.5 and the focal depth is ca. 20 km, the change in the rainfall threshold condition can be estimated by referring to ca. 15% in the JEA. When the magnitude is greater than 6.5, but focal depth is less than 15 km, we can refer to a threshold change of 26% in the LEA and WEA. When the DER exceeds the median DER, we may think the rainfall can reach a warning level at the first stage. However, earthquake-affected areas responded differently to the statistical approaches (Table 2), which may be attributed to the heterogeneity of rainfall for triggering debris flows under different surface conditions. Thus, the hourly I-D curve can be used. The degree of I-D curve lowering after a strong shock are referred in Table 2. When the mean hourly rainfall intensity is above the curve, a regional warning should be issued.

Due to the lack of meteorological in-situ observations, advanced satellite-based rainfall data can be used as an effective alternative for near real-time analysis, which is widely adopted for disaster research (Jia et al., 2020). The Global Precipitation Measurement (GPM) mission, led by the National Aeronautics and Space Administration and the Japanese Aerospace Exploration Agency has been the latest generation of rainfall products since March 2014 (Hou et al., 2013). With the resolution of 0.1° and 0.5 h, the up-to-date GPM products may be suitable for near real-time analysis based on long-term historical records, which have been expanded back to start-ups (in 2000) by calibration (Huffman et al., 2019). We use the gridded rainfall dataset to check the reliability of the new GPM data for future application in debris-flow monitoring and warning. Correlation coefficients of 0.67, 0.53, and 0.56 are obtained for Jiuzhaigou, Wenchuan, and Lushan areas, respectively, (Figure 6), which indicates that the reliability needs to be further improved, as also confirmed by Liu et al. (2019). Though any satellite-based method will cause inevitable uncertainties (Carr et al., 2015), a combination with the methods used in this study could be an important supplement for debris-flow warning in ungauged areas with earthquakes.

The 40 years gridded rainfall data can provide enough information for this study, but the 3 h resolution and GMT format could cause uncertainty for determining the accurate time of debris-flow occurrence. Furthermore, even if eliminating the effects of fluctuant annual rainfall, the rainfall thresholds cannot avoid abnormal distribution of rainfall within certain year. The statistics in small regions (specified high earthquake-intensity areas) depend on the local information and temporal variability (Nikolopoulos et al., 2017; Gariano et al., 2020). However, most debris-flow disasters always occur in places where there is insufficient or ineffective instrumental observation.

Figure 4 shows that effects of the Lushan and Jiuzhaigou earthquake in the curves are not very obvious as that of Wenchuan earthquake. I-D scatters obtained by other study also support the point (Guo et al., 2021). Guo et al. (2021) pointed that debris flows after Lushan earthquake are triggered by shorter-duration rainfall than in most other regions, including the Wenchuan earthquake area, which may magnify the uncertainty from the rainfall data. In addition, some regional I-D threshold is difficult to be obtained, due to the limited data which cannot meet demand for a rigorous fitting. That is why we emphasize more on the change in the I-D relationships rather than the accurate threshold.

Van Asch et al. (2014) made a link between the rainfall thresholds and sediment material delivered by seismic landslides retained in gullies. Thousands of landslides triggered by the Lushan earthquake have become the material source of debris flows (Tang et al., 2015). But the erosion of channel deposits by overland runoff after Lushan earthquake was the dominant mechanism of debris-flow formation in the LEA (Guo et al., 2021). Compared with the WEA, the debris-flow volume in the LEA is smaller, which may be due to the smaller earthquake magnitude and the wetter climate for vegetation recovery. In addition, free placement of wastes produced in post-quake reconstruction can be initiated more easily to form debris flows. The complex spatial heterogeneity of natural and anthropogenic factors makes great differences of critical rainfall conditions for debris flows in different regions. Even so, it is still difficult to isolate any other factors for discussing the earthquake effects on rainfall for triggering the debris flows.