2.1.1 Study area

China lies between latitudes 18 and 54^∘ N and longitudes 73 and 135^∘ E. With an area of about 9.6 million square kilometers, it is the world's third-largest country. The landscape varies significantly across this vast area, ranging from the Gobi and Taklamakan deserts in the north to the subtropical forests in the wetter south. The eastern plains and southern coasts are the location of most of China's agricultural land and settlements. The southern areas consist of hilly and mountainous terrain. The west and north of the country are dominated by sunken basins (such as the Gobi and the Taklamakan deserts), towering massifs and rolling plateaus, including part of the highest tableland on earth, the Tibetan Plateau. Based on its topography, China can be divided into six homogeneous geomorphological macro-regions (Wang et al., 2020): eastern plain, southeastern hills, southwestern mountains, north-central plateaus, northwestern basins and Tibetan Plateau. Mountains (33 % of the territory), plateaus (26 %) and hills (10 %) together account for nearly 70 % of the entire surface.

In recent years, the precipitation intensity has shown an increasing trend over China (Zhang and Cong, 2014). Influenced by the East Asian summer monsoon and the geomorphologic settings, the climatic condition across the whole country varies considerably (Wu et al., 2019). In general, the wet season in China lasts from May to September (Song et al., 2011b). In the eastern area, the annual rainfall decreases from south to north with an average annual precipitation that ranges from 250 to 750 mm (Zhang et al., 2007). In the west and central part of North China, due to its far distance away from an ocean, the climate tends to be more arid, and the landscape transitions to large deserts. The Tibetan Plateau is characterized by wet and humid summers with cool and dry winters. More than 60 %–90 % of the annual total precipitation falls between June and September (Xu et al., 2008).

2.1.2 Flash flood disaster inventory

The dataset used in this study has been collated and made accessible for the present research as part of a national effort carried out by the Chinese Institute of Water Resources and Hydropower Research (Liu et al., 2018). It reports flash flood occurrences in China from 1950 until 2015, together with available information, namely longitude and latitude, date, fatalities, and economic losses. Due to the lack of specific terminology or detailed descriptions of the disaster process in the database, the data do not differentiate the initial mechanism, be it water floods or debris floods/flows (e.g., Fernández and Lutz, 2010; Gartner et al., 2014). The only common information is that for each specific case, a large amount of overland flows, mixed with an unspecified solid fraction, rapidly flooded a given area with disastrous effects (e.g., Pierson et al., 1987; Chang et al., 2011).

To better understand the spatiotemporal dynamics of flash floods and associated disasters, as well as the relationship with the triggering factors, the date of occurrence is of vital importance. Therefore, for consistency reasons, we considered only the records whose metadata contained a full temporal description (year–month–day) resulting in a subset of 32 473 flash flood disasters (accounting for 68 % of the entire dataset) precisely located in space and time (Fig. 1).

Figure 1Spatiotemporal distribution of flash flood disasters in China.

2.2.1 Spatiotemporal K function

Ripley’s K function (K_(s)) is largely applied in environmental studies to analyze the pattern distribution of spatial point processes and to detect deviation from spatial randomness. K_(s) allows us to determine if a set of mapped punctual events show a random, dispersed or cluster distribution pattern over increasing distance values (Ripley, 1977). It is computed as the ratio between the expected number of events falling at a distance r from an arbitrary event and the average number of points per unit area, corresponding to the intensity of the spatial point process (λ). In the same way, it is possible to define the temporal K function (K_(t)) allowing us to assess the randomness of events in time. The spatiotemporal K function (K_(s, t)) is a generalization of the univariate Ripley’s K function which allows us to test for the independence between two variables, space (s) and time (t). Therefore, the K_(s, t) is a suitable tool to investigate the clustering behavior of a set of events occurring in a given area at a given time. For a point process X with intensity λ, according to Eq. (1), it is defined as the number of expected further events (E) occurring within a distance r and time t from an arbitrary event u, where a defines the contouring circle.

$$\begin{array}{}\text{(1)}& K_{(\mathrm{s},\mathrm{t})}=\mathrm{1}/\mathit{\lambda }\times E\left[n\right(X\cap a(u,r,t)u\left)\right|u\in X]\end{array}$$

To illustrate the interaction between space and time, it can be useful to evaluate the value D_(s, t) defining the difference between the spatiotemporal K function and the product of the purely spatial and the purely temporal K function (see Eq. 2).

$$\begin{array}{}\text{(2)}& D_{(\mathrm{s},\mathrm{t})}=K_{(\mathrm{s},\mathrm{t})}-K_{\left(\mathrm{s}\right)}\times K_{\left(\mathrm{t}\right)}\end{array}$$

If space and time are independent variables, this value equals zero. Otherwise, positive values of D_(s, t) indicate the interaction among events in space and in time. In other words, events closer in space are more likely to occur in a closer time. In contrast, the negative values mean a dispersed pattern.

In this study, spatiotemporal K function analyses were performed with the package “Spatial and Space-Time Point Pattern Analysis” (splancs; Rowlingson and Diggle, 2017) in R (R Core Team, 2019).

2.2.2 Spatiotemporal scan statistics

Scan statistics was originally developed by Naus (1965a, b) to detect clusters in a 1D point process. Subsequently Kulldorff (1997) extended this approach to multi-dimensional point processes, introducing the use of scanning windows. The procedure was implemented with free software, SaTScan™ (https://www.satscan.org/, last access: 25 April 2020), which can handle a purely spatial, purely temporal or spatiotemporal dataset and includes different probability models depending on the nature of the data and the scope of the research (e.g., for prospective or retrospective cluster detection). In the purely spatial case, the aim of scan statistics is the early detection of clusters, allowing us to map them and to assess their statistical significance. Moving windows scan the region, increasing their radius up to a fixed limit (R_max), and count the number of events falling inside and outside the area. The probability that a window contains more observations than expected is assessed via the likelihood ratio through a comparison with the background population. Then, the null hypothesis of randomness is tested via Monte Carlo simulations, based on repeated random sampling. The spatiotemporal scan statistics use cylinders instead of circular windows, in which the height of the cylinder accounts for the temporal dimension.

In order to deal with flash floods, the retrospective spatiotemporal permutation scan statistics (STPSS; Kulldorff et al., 2005) seems to be the most adequate model. Indeed, for environmental processes, the definition of the background population at risk needed for the statistical significance assessment of the detected clusters is quite problematic. STPSS assesses the expected number of cases using only the observed cases by permutation, supposing that each event has the same probability for all the times. Computationally, if C is the total number of observed cases and c_zd the number of cases observed in a specific zone z and on a day d, the expected number of cases per zone and day (μ_zd) is equal to the following:

$$\begin{array}{}\text{(3)}& {\mathit{\mu }}_{\mathrm{zd}}={\displaystyle \frac{\mathrm{1}}{C}}\left(\sum _{\mathrm{z}}{c}_{\mathrm{zd}}\right)\left(\sum _{\mathrm{d}}{c}_{\mathrm{zd}}\right).\end{array}$$

It follows that, for a spatiotemporal cylinder A, the expected number of cases μ_A can be estimated as the sum of each μ_zd inside the cylinder A:

$$\begin{array}{}\text{(4)}& {\mathit{\mu }}_{\mathrm{A}}=\sum _{\mathrm{z},\mathrm{d}\in \mathrm{A}}{\mathit{\mu }}_{\mathrm{zd}}.\end{array}$$

If C_A is the number of observed cases in A, considered as Poisson-distributed with mean μ_A, the Poisson generalized likelihood ratio (GLR) can be computed as follows:

$$\begin{array}{}\text{(5)}& \mathrm{GLR}={\left({\displaystyle \frac{c_{\mathrm{A}}}{{\mathit{\mu }}_{\mathrm{A}}}}\right)}^{c_{\mathrm{A}}}{\left({\displaystyle \frac{C-c_{\mathrm{A}}}{C-{\mathit{\mu }}_{\mathrm{A}}}}\right)}^{C-c_{\mathrm{A}}}.\end{array}$$

This ratio is calculated and maximized for every possible scanning cylinder. The cylinder with the highest GLR value is the most likely cluster, that is, the cluster least likely to be due to chance, while the following are secondary clusters. Then, Monte Carlo simulations are performed, and the statistical significance (p value) of the detected clusters can be assigned by comparing the rank (R) of GLR from the real dataset with the GLR from the simulated one. Thus, the p value can be estimated by dividing R by the number, plus 1, of performed simulations.

3.2.1 Cluster parametrization and their spatial distribution

Scan statistics were performed to detect spatiotemporal clusters of flash flood disasters. The size and the duration of the detected clusters are influenced by the input parameters of the scanning windows, namely the maximum radius (R_max), the maximum temporal duration (T_max) and the time aggregation (T_agg). Indeed, values of R_max exceeding the 50 % of the total area or, for T_max, the 50 % of the entire study period can result in an exceptionally low rate outside the scanning window rather than detecting an exceptionally high rate inside. T_agg is used to adjust the aggregation of the data over time and allows us to adjust for cyclic temporal trends: for example, a time aggregation of 1 year automatically adjusts for the seasonal variability, while the contrary happens with monthly aggregations. Moreover, both spatial and temporal aggregations can highly reduce the computer processing time. Different values for R_max were tested for the southeast and northwest areas in China, as suggested by looking at the respective perspective 3D plot. Nevertheless, the performed analyses indicated that the effect on the detected clusters were negligible and that finally the distribution of spatiotemporal clusters of flash flood disasters in the country can be analyzed as a whole. A set of possible combinations of R_max and T_max was tested, while T_agg was initially fixed to 1 year.

More specifically, since results of the K function revealed that flash flood disasters in the study area and investigated period are globally clustered even at short distances, we chose R_max of 100, 200 and 300 km and T_max equal to 1, 3 and 5 years. The choice for R_max is corroborated by Zhang et al. (2010) who report measurements constantly less than 500 km for the radius of typical convective storms in the Chinese mainland which can trigger flash floods. Results of STPSS for each of the nine combinations of these parameters are shown in Fig. 4.

Figure 4Significant (p<0.005) spatiotemporal clusters of flash flood disasters in China during 1950–2015.

Table 1Number of detected spatiotemporal clusters of flash flood disasters in China during 1950–2015 using different parameters, as indicated.

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As shown in Table 1, the largest variation in the number of detected clusters is mainly associated with R_max rather than with T_max; as R_max increases, the number of detected clusters decreases. Indeed, large R_max values affect the detection of clusters acting at a fine scale by merging small cluster close each others into big ones or eventually by neglecting very small flash flood aggregations. Conversely, very large clusters, acting at a coarse spatial scale, are detected for any value of R_max, as can be geographically visualized in the southeasternmost sector of China (Fig. 4). Changes in T_max have almost no effect on the number of detected clusters since, even allowing for a maximum duration of 5 years, almost all the clusters do not exceed the duration of 1 year.

To confirm this finding, we computed the temporal duration of the first 10 clusters of flash flood disasters detected by applying a T_max equal to 3 years and for the three models, defined by using values of R_max equal to 100, 200 and 300 km (Table 2). Results confirm that cluster duration, expressed as start and end dates, never exceeds 1 year. The most significant cluster (ranked as ID =1) is the same for any model and is dated to 1975. Secondary clusters (just from the second to the tenth) are almost the same using R_max of 200 or 300 km, while, reducing the radius to 100 km, their size and ranking can change due to the merging of small clusters into bigger ones. Finally, it is worth noting that the top 10 clusters are well distributed over the entire study period, with the oldest one detected between 1963 and 1969 and the latest in 2010.

Table 2Temporal duration of the first 10 clusters of flash flood disasters detected via three different models (left: R_max=100 km; center: R_max=200 km; right: R_max=300 km).

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We opted to carry out additional analyses using a T_agg of 3 months (hereafter referred as “monthly model”). Results are shown in Fig. 5 where information on the spatial distribution of the detected clusters is shown. Overall, the clusters chiefly appear along the main river systems in China, namely the Yangtze, the Yellow, the Pearl and the Yarlung Zangbo rivers. In addition, some clusters stand out on high mountains, such as the Qinling-Daba and the Changbai mountains.

Figure 5Significant (p<0.005) spatiotemporal clusters of flash flood disasters occurring in China during 1950–2015 (R_max=200 km, T_max=3 years, T_agg=3 months).

3.2.2 Temporal characterization of detected clusters

It emerges that clusters detected by using the different parameters for the scanning cylinders overlap both in space and in time. Therefore, in the present analysis, seeking to investigate in more details the years of occurrence and the temporal duration of detected clusters of flash floods, only results from the model with R_max=200 km, T_agg=1 year and T_max=3 years are presented. Considering all the statistically significant clusters, they emerged during almost each year of the investigated period but are more frequently starting from 1980. The relative small number of clusters detected between 1950 and 1980 may imply that the data acquisition and reporting in the Chinese database of hydro-morphological disasters were not fully operational at the time. Conversely, from 1980 to the present day the Chinese database has evolved into a mature and detailed geographic information system. Another factor explaining this distribution can be the more frequent extreme precipitation observed in recent decades, which could have increased the frequency of flash flood disasters in this last period. The precipitation regime can also explain the variation in the duration of the detected clusters. Indeed some clusters have a temporal extent up to 3 years, which could result from a persistent precipitation pattern over a delimited prone area.

Figure 6Temporal duration of flash flood disaster clusters detected via the “yearly model” (R_max=200 km, T_agg=1 year, T_max=3 years).

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To highlight the influence of the seasonal variability in cluster detection, we carried out additional analyses using a T_agg of 3 months (hereafter referred as monthly model). As shown in Fig. 5, the detected clusters are spread along the main river systems in China, namely the Yangtze, the Yellow, the Pearl and the Yarlung Zangbo rivers. In addition, some clusters stand out on high mountains such as the Qinling-Daba and the Changbai mountains.

Table 3Temporal duration of the first 10 clusters of flash flood disasters detected via the monthly model (R_max=200 km, T_max=1 year, T_agg=3 months).

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Forcing the model parameterization to aggregate over 3 months allows us to investigate potential seasonal effects. Indeed, even if the maximum temporal duration is still 1 year, looking at the 10 most significant clusters detected under the monthly model (Table 3), the result is that all of them have a duration of 3 (six clusters) or 6 (four clusters) months. Notably, almost every cluster (nine clusters) encompasses the period from July to September, with an earlier start date (in April) for the ones which have a longer duration.

To visualize the seasonality trend, we summarized these results using a cyclic representation (Fig. 7). The majority of the cluster have a 3-month duration, concentrated in the period between July and October. Furthermore, clusters of 6-month temporal duration are most likely to occur from January to July or from April to October. As for clusters with 9-month temporal duration, these mostly cover the period of July–August–September, irrespective of the starting month. Ultimately, as noticed for the yearly model, many more clusters were also detected in the monthly model in the recent period. Overall, the vast majority of flash flood disaster clusters happened between July and October, a period coinciding with the wet season in China.

Figure 7Seasonal effect of flash flood disaster clusters detected via the monthly model (R_max=200 km, T_max=1 year, T_agg=3 months).

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3.2.3 Clusters pattern evolution at decadal scale

The previous analyses allowed us to detect yearly and seasonal clusters. However, environmental changes usually act on a longer time span. To better investigate this factor, we considered a temporal subdivision of the dataset into six subsets, each one lasting 10 years (starting from 1956). Each subset was analyzed separately using the following parameter for the scanning widows: R_max=200 km and T_max=1 year, while no temporal aggregation was applied. This allowed us to precisely evaluate the temporal duration of each cluster, given as number of days between the earliest and the latest flash flood single event within a cluster. As shown in Fig. 8, the number of detected clusters increases from the early to recent periods. These are compared with the rainfall distribution derived from the daily rainfall data provided by the China Meteorological Administration (http://data.cma.cn/, last access: 30 November 2020). In the present study, only the weather stations (a total of 699 rain gauges) with complete data for the period 1955–2015 were considered. From these, we computed the extreme precipitation as follows. Out of the rainfall records available per weather station, we initially extracted 5 % of the time series corresponding to the rainfall values greater than the 95th percentile (Karl and Easterling, 1999; Klein Tank and Können, 2003). Then we cumulated these values per station over decadal time periods corresponding to 1956–1965, 1966–1975, 1976–1985, 1986–1995, 1996–2005 and 2006–2015. From these cumulated extreme rainfall values per station and per decade, we computed the mean over the 10-year time span and then interpolated over the whole spatial domain under consideration via a ordinary kriging. The data were regionalized on a 2 km × 2 km lattice. The procedure returned six maps of the mean extreme events per decade over the Chinese territory. The result is that flash-flood-detected clusters are mainly located in the southeasternmost humid regions in every period. However, in the last 2 decades, clusters appear also in the northwestern arid regions. Even if the rainfall distribution, averaged over each decade, does not allow to discover clear changes along the subsequent periods, these newly detected clusters can be due to the intensification of the extreme rainfall events occurring in the area in recent periods. This assumption is confirmed by the statistics on cluster duration (Fig. 9). From the boxplot summarizing the descriptive statistics it is evident that the median values of cluster durations tend to slightly decrease from 46 d (1956–1965) to 17 d (1986–1995) and stabilize at a value around 20 d in the last 2 decades. At the same time, the overall duration, measured as the difference between the maximum and the minimum value, is higher in the late periods (140 d in 1956–1965 and 93 and 74 d respectively in the 2 following decades) than in the early periods (about 65 d for the last 2 decades). This is even more evident looking at the inter-quantile ranges, which decrease with time. To resume, from these analyses, the result is that the number of detected clusters globally increases in time, but their duration drastically decreases in the recent period.

Figure 8Significant (p<0.005) spatiotemporal clusters of flash flood disasters in China every 10 years. The size of the circles indicates the spatial coverage of the flash flood clusters we detected.

Figure 9Boxplots summarizing the descriptive statistics of the duration of clusters reported in Fig. 8.

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Spatiotemporal clusters of flash flood disasters detected in China by decade were further assembled in a unique image. To this end, the centroid of each cluster (with reference to Fig. 8) was extracted and intersected with the catchment boundaries. Then, we computed the total number of clusters per catchment (Fig. 10a), as well as the average interval of time at which two consecutive clusters were detected in the same catchment (Fig. 10b). The result is that the catchments mainly affected by clusters of flash floods throughout several decades are mainly located in the southeast sector and essentially in the coastal mountains and that, on average, most of the clusters occur within an interval of 10–20 years.

Figure 10Number of times a cluster has been detected per catchment and by decade (a). Average time interval between two clusters detected over the same catchment by decade (b).