Spatial–temporal characteristics and driving factors of flash floods in Shaanxi Province considering regional differentiation

Flash floods show strong regional differentiation in spatial–temporal distribution and driving forces, thereby hindering their effective prevention and control. This study analyzed the spatiotemporal characteristics of flash floods in Shaanxi Province, China, differentiated among the northern Shaanxi (NS), Guanzhong (GZ), and southern Shaanxi (SS) regions based on the Mann–Kendall, Theil–Sen Median, and standard deviation ellipse methods. The main factors driving disasters and their interactions in each region were then identified within the three categories of precipitation factor (PPF), surface environment factor, and human activity factor (HAF) based on a geographical detector. Finally, the differences in flash flood characteristics among the NS, GZ, and SS regions were analyzed. The results showed that flash floods in Shaanxi Province are greatly affected by the PPF and the HAF, although the spatial–temporal characteristics and disaster-causing factors were significantly different in each region. The regions were ranked according to the number and growth trends of flash floods as follows: SS.GZ.NS. Furthermore, flash floods were affected by multiple factors, with the interaction between factors acting as a driving force of flash floods. The results of this study can provide a reference for the management of flash floods under regional differentiation.


INTRODUCTION
Flash floods are considered to be the type of natural disasters of extremely high risk due to their characteristics of sudden occurrence, rapid formation, and strong destructiveness. Many countries globally are affected by flash floods (Trigo et al. 2016;Ngo et al. 2021). Over 60,000 flash flood disasters have been reported in China since 1949, which resulted in great casualties and economic losses (Liu et al. 2018). Flash floods have strong geographical differentiation, with their characteristics and disaster-causing factors varying from region to region (Hou et al. 2020;Xiong et al. 2020). Therefore, revealing the characteristics of flash floods in different regions is of great significance for preventing and mitigating hazards resulting from flash floods.
Flash floods are affected by multiple factors, including precipitation, surface environment, and human activities (Arora et al. 2021). Quantitatively and accurately revealing the characteristics and drivers of flash floods present a great challenge due to regional differentiation (Adnan et al. 2019). The analysis of the spatial and temporal variation and driving factors of flash floods is the basis for scientific understanding of the distribution and mechanism of the formation of flash floods and is further necessary for the management of flash floods under regional differentiation.
The Mann-Kendall (M-K) test is widely used to explore temporal and spatial distribution characteristics and is used in trend analysis and mutation point tests due to its insensitivity to abnormal values (Seenu & Jayakumar 2021). The Theil-Sen Median (Sen) estimation method is also a commonly used nonparametric trend test method. The combined M-K and Sen (MK þ Sen) test is an important method used to assess the trend of a time series since this method is insensitive to data errors and has a solid statistical theoretical basis for testing the significance level (Phuong et al. 2020;Shi et al. 2021). In addition, the standard deviation ellipse (SDE) is an important method for reflecting spatial characteristics, such as the central trend, discrete trend, and directional trend (Yang et al. 2021). Shi et al. (2018) used the SDE and MK þ Sen to analyze the spatiotemporal characteristics of PM2.5 (particulate matter with a diameter of 2.5 μm) from 1999 to 2014. Wang et al. (2021) used the transfer matrix in combination with the SDE and spatial autocorrelation analysis to analyze the influence of land use and land cover on the spatiotemporal pattern of precipitation.
The geographical detector is a new statistical method used to reveal the driving forces of a certain spatial distribution. The method was first proposed by Wang Jinfeng and can detect both numerical and qualitative data (Wang et al. 2016). Using the geographical detector, the power of a single independent variable to explain the variation in a dependent variable as well as the power of the coupling of the spatial distributions of two independent variables to explain the variation in the dependent variable can be detected. Recent studies have used geographical detectors to analyze the driving forces of flash floods (Xiong et al. 2020).
Realizing the effective prevention and control of flash floods under regional differentiation in the same administrative region requires certain prerequisites (Singh et al. 2008). These include analyzing the changes in the properties of flash floods before and after sudden change, identifying changes in the intensity and evolution of flash floods at different spatial scales, and detecting the driving forces of flash floods and the synergistic effects between them. Therefore, an in-depth analysis of the temporal and spatial distributions of flash floods under regional differentiation and the quantification of disaster-causing factors are necessary.
Shaanxi Province, China, shows a strong regional differentiation in climatic conditions, with a semi-arid area in northern Shaanxi (NS), a semi-humid area in Guanzhong (GZ), and a humid area in southern Shaanxi (SS). This present study applied the M-K, MK þ Sen, and SDE methods to the historical data of flash flood disaster events in Shaanxi Province from 1949 to 2015 to analyze the spatial and temporal distributions of flash floods in the NS, GZ, and SS regions. Second, the present study quantified the influences of the precipitation factor (PPF), the surface environment factor (SEF), and the human activity factor (HAF) and their interactions on flash floods in the NS, GZ, and SS regions using the geographical detector. Finally, the differences in flash flood disaster characteristics and the explanatory power of different factors under regional differentiation were analyzed. Figure 1 shows the research framework followed under the current study. The results of the present study can provide a reference for the prevention and mitigation of flash floods in Shaanxi Province.

METHODOLOGY M-K statistical test
The M-K statistical test is applicable for both trend analysis and assessing mutation in a time series. Since the M-K is insensitive to abnormal values and human factors, it has been widely used in time-series analysis within hydrology and meteorology (Nyikadzino et al. 2020). The M-K test can be implemented through the following steps: Step 1: Constructing a order sequence of time series for k samples: In Equations (1) and (2), sign is the express sign function, X i is the express random variable and is composed of i elements (i ¼ 1, i þ 2,…, k), and X j represents other random variables comprising j elements ( j ¼ 2,…, k À 1).
Step 2: Assuming a random time series, the definition of UF k is: Step 3: Composing the value of UF k into a curve UF.
The processes outlined in step 2 are repeated for the inverse sequence, and the curve UB can be obtained with UF ¼ À UB. The UF and UB refer to the coordinate system. The testing of trends is conducted at the specific t 0 significance level (t 0 ¼ 95% was chosen in the present study, the null hypothesis of no trend was rejected if | UF k | . 1.96). A curve UF within t 0 indicated a significant trend in the time series, with UF . 0 and UF , 0 indicating an upward and downward trend in the time series, respectively. The intersection of the curves UF and UB in the confidence interval indicated a possible mutation point.

Theil-Sen Median
The Theil-Sen Median trend analysis (Sen) is a robust nonparametric trend calculation method, which can reduce the influence of data outliers. Sen assesses the trend and degree of the sequence by calculating the median of the slope of the data combination. Sen can be expressed using the following formula :

Uncorrected Proof
In Equation (6), S is the variation trend of the flash flood, x k and x i are the sequence values for k and i periods, respectively, and Median(·) is the median function. S . 0 and S , 0 indicate an upward and downward trend in the time series, respectively.
The M-K test can be combined with the Sen (MK þ Sen) to assess the trend of time series, with this approach often used in hydrology and meteorology (Esmaeilpour et al. 2021;Syed et al. 2021). The present study used the MK þ Sen to detect the variations in flash floods over time.

SDE analysis
The SDE analysis can express the spatial characteristics of a variable by calculating the standard distance from a set discrete point to the average (Peng et al. 2016;Shi et al. 2018). Therefore, the present study used the SDE to identify the change in the center position and the moving trend of flash floods. The specific expression is: In Equations (7) and (8), (x i , y i ) is the coordinate of variable i, (x mc , y mc ) is the arithmetic mean center of the variable, and n is equal to the total number of variables. (SDE x , SDE y ) is the coordinate of the center of the ellipse.
The angle of rotation is calculated as follows: In Equations (9)-(12), xx i and yy i are the deviations from the x-axis and y-axis to the mean center, respectively.

Geographical detector
The geographical detector method is based on the geographical spatially stratified heterogeneity theory. The method is able to interpret the degrees to which a different impact factor X explains Y by detecting the relationship between X and the spatial change in Y. The geodetector method uses four different detectors (Wang et al. 2010). The present study applied the factor detector and the interaction detector to detect the main factors influencing flash floods.

Factor detector
The factor detector was used to detect the degrees of explanation between impact factor X and the spatial differentiation of Y according to the rate of local variance to the global variance. The expression is: In Equation (13), q is the degree to which the impact factor X explained the spatial differentiation in Y (0 q 1), k ¼ 1,…l represents the number of partitions of the impact factors X, N k is the number of units in the kth partition of the impact factors X, N is the number of all units of X, s 2 is the global variance of Y, and s 2 k is the local variance of Y in the kth partition.

Interaction detector
The interaction detector can assess the explanatory power of the interaction factor to Y through space superposition technology. Here, X1 and X2 are different influencing factors, X1 ∩ X2 represents the spatial superposition of X1 and X2, and q(X1 ∩ X2) represents the degree to which the interaction factor explains the spatial differentiation Y. As shown in Table 1, the interaction relationship of factors was determined by comparing the explanatory powers of q(X1), q(X2), and q(X1 ∩ X2).
The power of each driving factor to explain the variance in flash floods can be identified through the following steps: (1) sampling points are established for each partition; (2) continuous driving forces are divided into 10 classes according to the natural break method; and (3) the density and driving factors of flash floods for each region are extracted by sampling points and the powers of each driving factor and each combination of interacting driving factors were calculated by the geographical detector. In addition, the average value of each driving factor is used for driving factors with multi-year data to calculate the power of each driving factor to explain flash floods.

OVERVIEW OF THE STUDY AREA AND DATA PREPARATION Study area
Shaanxi Province (105°29 0 -111°15 0 E, 31°42 0 -39°35 0 N) is in the northern part of central China and has a total area of 2.056 Â 10 7 km 2 . The altitude of the province decreases from north to south, showing obvious spatial zoning. The 'North Mountain' (a series of limestone-based rocky hills in the transition zone between the southern margin of the NS Loess Plateau and the GZ Basin) and Qinling Mountains can act as a boundary dividing Shaanxi Province into the following three natural regions: (1) the NS Loess Plateau; (2) the GZ Basin; and (3) the SS Qinba Mountain.
The different regions of Shaanxi Province show considerable differences in topography, geomorphology, climate, population distribution, and so on. The NS Loess Plateau is characterized by an altitude, average annual temperature, average annual precipitation, and population of 900-1,900 m; 7-12°C; 400-550 mm; and ∼5.9 million, respectively, whereas the corresponding characteristics of the GZ Basin are 190-850 m, 12-14°C, 500-800 mm, and ∼25.9 million, respectively, and that of the SS Qinba Mountain are 500-3,767 m; 14-16°C; 700-900 mm; and ∼7.7 million, respectively. These regional differences in characteristics result in spatial-temporal and hazard-level differences in flash floods among the different regions. Therefore, an in-depth analysis of the distribution and driving factors of flash floods in the three regions of Shaanxi Province is required. Figure 2 shows an overview of the study area and the spatial distribution of historical flash floods. The data used for Shaanxi Province in the present study included historical flash flood disaster data, the PPF, the SEF, and the HAF. The datasets were mainly obtained from the Flash Flood Investigation and Evaluation Dataset of Shaanxi Province (FFIEDSP), the National Meteorological Information of China (CMA, http://www.resdc.cn), the Geospatial Data Cloud (GDC, http://www.gscloud.cn), and the Resource and Environment Science and Data Center (RESDC, http://www.nmic. cn) ( Table 1).
The present study used daily precipitation data as monitored by meteorological stations in Shaanxi Province and its surrounding areas from 1949 to 2015. The PPF was calculated by the following equation (Liu et al. 2017): In the above equation, m is the number of years and y is the index of each year, n is the number of precipitation days in a year, R d is the daily precipitation on day d, R i ¼ 25, 50, or 100 mm, corresponding with the threshold of the ith precipitation index of daily precipitation, and Pi is the precipitation indicator under R i for each meteorological station.

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The SEF included the digital elevation model (DEM, unit: m), the slope (SLOPE, unit:°), the soil type (SOIL, unitless), the normalized difference vegetation index (NDVI, unitless), and the vegetation type (VEG, unitless). The DEM, SLOPE, and NDVI were used to reflect topographic relief features, steepness of the surface, and vegetation cover, respectively, whereas the SOIL and VEG were closely related to the precipitation runoff process. Every indicator has a relationship with flash floods.
The HAF included the population density (PD; unit: person/km 2 ), the density of gross domestic product (GDP; unit: 10 4 yuan/km 2 ), the density of villages along the river point (VD; unit: village/km 2 ), and the land use/land cover change (LUCC; unitless). The LUCC was included in the HAF since the LUCC is mainly affected by human activities (Chen et al. 2020;Yu et al. 2020).

Spatial-temporal characteristics of flash floods
The present study analyzed the inter-annual, intra-annual, and inter-decadal variation of flash floods in different regions of Shaanxi Province. Spatial analysis of flash floods was based on the M-K, Sen, and SDE methods during which the trends in spatial variation and variation in the center of gravity of flash floods were analyzed, respectively.  Figure 3A(b) shows that the mutation points of NS were in 1972 and 1999 (the intersection point of the UF and UB). A comparative analysis showed that a more obvious average value of abrupt change occurred after 1972 ( Figure 3A(a)). Therefore, the mutation point of NS was 1972. Similarly, Figure 3B(b) and C(b) shows the mutation points of GZ and SS in 1981. A comparative analysis of the number of flash floods before and after the mutation year was performed in each region to further explore the evolution of flash floods over time. As shown in Figure 3A(a), B(a) and C(a), the mean numbers of flash floods before and after the mutation year in the NS were 1 and 3, respectively, whereas those in the GZ were 3 and 9 and those in the SS were 3 and 16, respectively. There was a significant change in the mean number of flash floods in each region before and after the mutation year. The number of flash floods after the mutation exceeded that before the mutation by a factor of 3-5. The rank of the regions in terms of the acceleration in the growth rate in flash floods was SS . GZ . NS.

Intra-annual variability in flash floods
The present study analyzed the concentration of flash floods in each year. As shown in Figure 3A(c, d), B(c, d), and C(c, d), flash floods in Shaanxi Province were mainly concentrated from May to October. There was no significant change in the intra-annual distribution of flash floods before and after the mutation in each region. The flash floods in NS were mainly concentrated during July to August, whereas those in GZ and SS were from June to September and June to October, respectively. However, there was a significant difference in the number of flash floods, and the annual cumulative maximum after the mutation exceeded that before the mutation by a factor of 3-6. The cumulative maximum number of flash floods in NS and SS after the mutation year was 60 and 136, respectively, and occurred during July. The highest numbers of flash floods in GZ occurred in July and August at 98 and 100, respectively. showed an increasing trend during the seven decadal periods from the 1950s to 2010s. In particular, the number of flash floods showed a significant increasing trend after the 1980s. The highest increase in flash floods occurred in SS. In addition, the frequency of flash floods in NS was lower than that in SS and GZ during each decadal period.

Trend in spatial variation
The spatial distribution of flash floods in Shaanxi Province was analyzed based on the MK þ Sen method. The trends in variations in S were divided into three categories: (1) a stable trend (from À0.0001 to 0.0001); (2) a decreasing trend (,À 0.0001); and (3) an increasing trend (.0.0001). At the same time, values which did not show a variation trend (absolute value of the M-K , 1.96) and other values that represented significant variation trends were noted. Table 2 shows a summary of the five categories of spatial variation trends.
The proportions of flash floods following within the different classifications in each region were calculated. Figure 4 shows the distribution of spatial trends in each region. There was a 'no obvious change' trend in flash flood disaster in .80% of the area in NS, whereas 12.44% of the area showed a 'moderate growth', mainly in the northeast. In GZ, 30.74% of the area showed a 'moderate growth' in flash flood disaster, whereas 28.97 and 5.3% of the area showed 'no obvious change' and 'rapid growth', respectively. There was a 'no obvious change' in flash flood disaster in 42.16% of the area of SS, whereas 'moderate growth' and 'rapid growth' collectively accounted for ∼42.46% of the total area, mainly in the southeast. Overall, there was an increasing trend in flash floods in Shaanxi Province, with a relatively large proportion of area showing a 'moderate Uncorrected Proof growth' in flash floods, mainly concentrated in the GZ, whereas 'rapid growth' was mainly concentrated in the SS. There was a gradual increase in flash floods in the NS, in which the risk of flash floods was relatively small compared with that in the other two regions.

Evolution of flash floods
The spatial patterns in flash floods in each region from the 1950s to 2010s were analyzed using the SDE method. As shown in Figure 5, the orientation angles in the NS, GZ, and SS regions ranged from 142.92°to 9.83°, 78.83°to 71.73°, and 68.66°to 100.23°, respectively. The track of the gravity center indicted a shift in the gravity center from the northwest to the southeast in NS, west to the east in GZ, and north to the south in SS. The oblateness of the ellipse of flash floods during each period in the three regions indicated that the directionality transfer of flash floods in NS was the most significant, followed by that in SS, whereas that in GZ was the least. The SDE area in the NS, GZ, and SS regions ranged from 63,393 to 32,336 km 2 ; 23,506 to 35,183 km 2 ; and 35,183 to 20,069 km 2 , respectively. The results showed that the SDE area of flash floods in each region decreased, indicating that the frequency of flash floods was higher and more concentrated.

Analysis of the factors driving flash floods
There are 12 factors driving flash floods, categorized into the PPF, SEF, and HAF. The current study calculated the power of each driving factor and interactions between driving factors to explain flash floods after mutation in the different regions.

Precipitation factors
Mutations in the flash floods occurred at different time scales among the different regions. Therefore, the present study analyzed precipitation data after the mutation. Three precipitation indicators, P25, P50, and P100, were calculated according to Equation  (14) to characterize the driving effect of moderate rain, heavy rain, and rainstorms on flash floods considering the actual situation and precipitation classification standard. The Kriging interpolation method was used to obtain the spatial distribution of continuous data of different precipitation intensities in each region. As shown in Figure 6, the average root mean square error values of different precipitation intensities in the NS, GZ, and SS regions were 0.23, 0.41, and 0.39, respectively. These results indicated that the interpolation results can accurately reflect the spatial distribution of precipitation intensities in different regions. As shown in Figure 6, precipitation intensity increased from NS to SS. Higher values of P25 were concentrated mainly at the boundary of each region, whereas higher values of P50 were distributed in the central part of the NS, southern GZ, and SS regions, respectively. Higher values of extreme weather (P100) showed a lower distribution throughout Shaanxi Province, mainly concentrated in SS.

Surface environmental factors
The DEM, SLOPE, SOIL, NDVI, and VEG were selected as the SEF. Figure 7 shows the spatial distribution of all indicators. As shown in Figure 7, the indicators in Shaanxi Province displayed obvious regional differences. The elevation of Shaanxi

Uncorrected Proof
Province is high in the north and low in the center. Initial soil, semi-luvisols, and luvisols are the main soil types in the NS, GZ, and SS regions, respectively. As SS contains many types of vegetation, vegetation cover in this region is relatively complex. In contrast, NS and GZ contain relatively simple vegetation cover, with cultivated vegetation accounting for most vegetation. Within the regions, the NDVI increases from NS to SS.

Human activity factors
The HAF not only increase the risk of flash floods but also act as an indicator of the degree of potential damage resulting from flash floods. Therefore, the present study selected VD, LUCC, PD, and GDP as the HAF. Figure 8 shows the categories and distributions of all the indicators. As shown in Figure 8, there were a clear regional difference in the HAF, with the VD along the river in NS and SS exceeding that in GZ, whereas PD and GDP were mainly concentrated in the GZ Plain. Cultivated land accounts for a large proportion of the LUCC in Shaanxi Province, thereby providing a favorable environment for the occurrence of flash floods.

Powers of the driving factors for explaining flash floods
The power of each driver and that of their interactions to explain flash floods in the different regions were obtained based on the geographic detector method. The P-values obtained were ,0.01, indicating that the power of each factor to explained flash floods was significant. The powers of the interacting driving factors to explain the spatial patterns of flash floods in the NS, GZ, and SS regions are shown in Figure 9.

Northern Shaanxi
As shown in Figure 9(a), flash floods in NS were most affected by precipitation. The power of rainfall factors to explain the spatial pattern of flash floods exceeded 25%, with P25 playing a major role. The NDVI was the driving factor in the SEF, with the highest Uncorrected Proof power to explain flash floods. This could mainly be attributed to the position of NS in the Loess Plateau in which serious soil erosion occurs. The VD was the driving force in the HAF, with the most power to explain flash floods. This result could be attributed to the direct relationship between the VD and the spatial pattern of flash floods. The results of the detection of the power of interactions between factors to explain flash floods showed that the powers of PPF ∩ SEF and PPF ∩ HAF to explain flash floods were significantly higher than those of SEF ∩ HAF. The powers of P25 ∩ VD, P100 ∩ VD, and P50 ∩ P100 to explain flash floods exceeded those of others' interactions, indicating that precipitation has a greater impact on flash floods in NS.

Guanzhong
As shown in Figure 9(b), the rank of rainfall factors in terms of the power to explain flash floods was as follows: P50 . P100 . P25. The maximum explanatory power of P50 was 0.13. The rank of surface factors to explain flash floods was as follows: DEM . SOIL . NDVI . VEG . SLOPE. This result could be attributed to flash floods mainly being concentrated in the junction area of mountains and plains and along the river. During flash floods, areas of low elevation are more vulnerable to flooding. Among the HAF, the GDP and POP showed strong powers to explain flash floods. This result could be attributed to the large PD of GZ, resulting in human activities having a strong impact on flash floods. Among the interactions  in driving factors, P50 ∩ P100 (q ¼ 0.37) showed the strongest power to explain flash floods, indicating that heavy rainfall is the key factor driving flash floods in the GZ area. In addition, there were relatively strong interactions between impact factors for P25 ∩ VD (q ¼ 0.33), P25 ∩ NDVI (q ¼ 0.27), and DEM ∩ VD (q ¼ 0.26). In general, the powers of interactions between the PPF and SEF and between the PPF and HAF to explain flash floods exceeded that of the interaction between the SEF and HAF. An analysis of the drivers of flash floods showed that historical flash floods in GZ were mainly as a result of the joint action of multiple factors, with these interactions increasing the risk of flash floods.

Southern Shaanxi
As shown in Figure 9(c), among the PPF, the power of P25 to explain flash floods exceeded that of P50 and P100. The DEM and VEG were the main driving factors of flash floods among the SEF. The HAF showed a high power to explain flash floods in SS, with the explanatory powers of the GDP and VD being 0.23 and 0.19, respectively. This result could mainly be attributed to the population being the main factor subjected to disaster during a flash flood.
The results showed that among the interactions between driving factors, those between the POP and GDP had the greatest interactive power to explain the flash floods of 0.53. The results showed that flash floods in SS have the potential to result in considerable losses. Besides, the interactions between various driving factors showed a high potential for driving flash floods. Therefore, flash floods in SS are relatively complex and are affected by multiple factors.

Spatial-temporal variation in flash floods
The present study showed the spatial-temporal distributions of flash floods in three regions of Shaanxi Province. There were increasing trends in the numbers of flash floods in each region. The numbers of flash floods increased in NS after the 1970s and in GZ and SS after the 1980s, consistent with the previous research results (Liu et al. 2018). The possible reasons for this result include the following: (1) the original underlying surface features changed due to increased human activities; (2) the increases in the frequency of extreme precipitation events; and (3) a lack of records for flash floods before the mutation periods. There were no significant differences in the intra-annual distributions of flash floods among the NS, GZ, and SS regions, with flash floods concentrated during the flood season. The frequency of flash floods was the highest during July, indicating a strong correlation between flash floods and precipitation.
The increasing trends in flash floods were different among the different regions. The increase in flash floods was most obvious in SS, followed by GZ, with that in NS the weakest. These differences between regions could be attributed to precipitation being the main driver of flash floods. The significant differences in the spatial and temporal distributions of precipitation between each region could be attributed to the unique climatic conditions and geographical environment of each region. Consequently, there were differences in the spatial and temporal distribution of precipitation among each region, leading to a gradual increase of precipitation in Shaanxi Province from north to south. The results of the SDE indicated that the distributions of flash floods in each region showed different directions among the different periods, with the patterns of distribution increasingly obvious and more concentrated from the 1950s to 2010s. High-intensity precipitation and human activities were the characteristics of areas in which flash floods were concentrated. Therefore, it can be concluded that the main drivers of flash floods are precipitation and human activities.

Factor detection
A further exploration of the main drivers of and differences in flash floods between the NS, GZ, and SS regions was required to increase the prevention and control of flash floods in Shaanxi Province. Figure 10 shows a comparison of driving factors identified for the three regions. As shown in Figure 10, the PPF played a major role in the occurrence of flash floods. Flash floods in NS and SS were mainly driven by moderate precipitation, whereas GZ was greatly affected by an intense precipitation. This result could be mainly attributed to a large area of GZ being located in the plain area in which the runoff rate is slow when precipitation intensity is weak.
Among the SEF, the NDVI and SLOPE showed the greatest powers to explain flash floods in NS. This result could be mainly attributed to NS being in the Losses Plateau in which there is less vegetation coverage and a large slope. Precipitation tends to result in soil erosion, which promotes the occurrence of flash floods. There were large differences between SS and NS in terms of surface factors explaining flash floods, and beside for the NDVI, other surface indicators showed relatively high powers to explain flash floods. This result could be attributed to the high, complex, and diverse vegetation coverage in SS. Flash floods are affected by the comprehensive effects of the SEF.
Among the HAF, the VD was the factor indicating the greatest vulnerability to flash floods. The POP and GDP also showed strong powers to explain flash floods in areas in which flash floods have a great impact on casualties and property losses. It is noteworthy that the GDP and POP in GZ were significantly higher than those in the other two regions. However, Figure 10 shows that the powers of these two indicators to explain flash floods were weak, whereas those of the DEM and SOIL were strong. This result could be mainly attributed to flash floods in GZ mostly occurring at the junction of the mountains and plains in which the PD is relatively low.

Detection of interactions
The interaction detector allowed the powers of interactions among different factors to enhance flash floods in each region to be identified. The proportions of nonlinear enhancement in factor interaction in the NS, GZ, and SS regions were 73, 97, and 91%, respectively. This result showed that flash floods in GZ and SS were affected by multiple factors, presenting a more complex situation than that in NS. Figure 11 shows the comparative result of the interaction detector for the three regions. NS showed a stronger interaction among driving factors, which could mainly be attributed to the relatively large power of a single indicator to explain flash floods, after which the enhancement by interaction resulted in the strengthening of the explanatory power. Although there were weak interactions between factors in GZ, their powers to explain flash floods were relatively concentrated. The interactions between factors in SS were similar to that in GZ, although the powers of interactions to explain flash floods were larger in SS.
The above analysis showed differences in the main forces driving flash floods among the different regions. However, the flash floods in Shaanxi Province are greatly impacted by the combined effects of precipitation and human activities. Precipitation is required for the formation of flash floods, whereas human activities indicate vulnerability to flash floods. Therefore, these factors have strong correlations with the occurrence of flash floods. In addition, population growth and urban expansion have resulted in changes to the surface environment since the 1980s, thereby shortening the time taken for runoff formation and increasing the incidences of flash floods (Cortes et al. 2018).
Therefore, certain strategies should be implemented to control and mitigate flash floods according to the main factors driving flash floods in different regions. These include strengthening the forecast of rainfall of different intensity, proving an early warning of flash floods, and implementing the timely evacuation of residents of villages along the river. In addition, the vegetation coverage in NS should be strengthened to reduce soil erosion.

Limitations of the present study
The present study analyzed the spatial-temporal distributions and flash flood driving factors and their explanatory power in Shaanxi Province. However, insufficiencies in the current study remain. First, the daily precipitation data used in the current study do not accurately reflect the impact of short-term heavy precipitation on flash floods. Second, there may be strong correlations between the different drivers of flash floods. Therefore, there is a need to further explore the sensitivity of flash floods to each driving factor. Despite these shortcomings, the present study provides a preliminary reference for the spatial and temporal distribution pattern of flash floods in Shaanxi Province and can improve public awareness of flash floods.

CONCLUSIONS
This present study quantitatively explored the spatial and temporal distributions of historical flash floods in the NS, GZ, and SS regions of Shaanxi Province from 1949 to 2015 based on the regional heterogeneity in flash floods. The powers of the main PPF, SEF, and HAF and their interactions to explain flash floods in each region were revealed. The differences in the distribution and driving factors of flash floods in three regions were compared and analyzed. The following conclusions were drawn: • There were obvious increasing trends in flash floods in Shaanxi Province among the different regions, with flash floods mainly concentrated in July and August. The rank of the regions in terms of the number of disasters and the growth trend was as follows: SS . GZ . NS. Moreover, disasters become increasingly concentrated after mutation.
• The forces driving flash floods in the NS, GZ, and SS regions were mainly related to precipitation intensity and human activities, although there were some differences among the regions. The flash floods in GZ and SS were the result of multiple factors, with the superposition effect of nonlinear enhancement exceeding 90%. However, individual driving factors had the greatest power to explain flash floods in NS and were mainly related to moderate rain intensity and the NDVI.
• Further study is required to extend the results of the present study, including the influence of short-term heavy rainfall and equifinality among different parameters on the driving force of flash floods. However, the results of the present study provide a preliminary basis for the prevention and mitigation of flash floods in Shaanxi Province, and corresponding preventative measures can be implemented according to the drivers and characteristics of flash floods in different regions.