*2.3. Methodology*

#### 2.3.1. Temporal Pattern

To explore the temporal pattern of flash floods in Yunnan, we analyzed the characteristics of year and month in this study, wherein we calculated the characteristic of year by the package "changepoint" in R software (R Core Development Team, R Foundation for Statistical Computing, Vienna, Austria), which implements various mainstream and specialized changepoint methods to find single and multiple changepoints within data [38]. The month characteristic was analyzed (from January to December) by the year characteristic.

### 2.3.2. Spatial Pattern

### (1) Kernel density estimation

In this paper, kernel density estimation techniques were used for establishing representations for the flash floods, since the kernel function can regard this estimate as averaging the impact of a kernel function centered at the flash flood point and evaluated at each point. We calculated spatial intensity of the flash floods using a kernel density estimation:

$$\lambda\_h(P) = \frac{1}{nh} \sum\_{i=1}^{n} k \left( \frac{P - P\_i}{h} \right) \tag{1}$$

where λ*h*(*P*) is the estimated spatial intensity of the flash floods, *P*1, · · · , *P<sup>n</sup>* are the locations of *n* observed flash floods, *k*(.) is the kernel, a meristic but not necessarily positive function that unites to one, and *h* is the bandwidth and determines the radius of a circle centered on *P* that the flash flood points *P<sup>i</sup>* will contribute to the intensity λ*h*(*P*). We calculated the spatial density of the flash floods to conduct the kernel density estimation in ArcGIS 10.2 and determined the search radius (bandwidth) based on the mean random distance (RD mean) calculations [39].

#### (2) Spatial mismatch analysis

Spatial mismatch analysis has a profound impact in the economy to measure misbalance between two spatially distributed factors, like unemployment and job distribution etc. In this study, the spatial distribution of number of flash floods in different time periods was taken as the input factor. We used spatial mismatch analysis to measure the imbalance between the number of flash floods in two different time periods. The formula is given as follows [40]:

$$SMI\_i = \left(\frac{B\_i}{\sum\_{i=1}^n B\_i} - \frac{F\_i}{\sum\_{i=1}^n F\_i}\right) \times 100\tag{2}$$

where *SMI<sup>i</sup>* expresses the spatial balance of city *i* between the number of the flash floods in two different time periods, *F<sup>i</sup>* and *B<sup>i</sup>* refer to the number of flash floods during start and end time periods. To judge whether the spatial relationship of the number of flash floods in two time periods was balanced, we selected a standard value to assist us by Jenks Natural Breaks Classification, which has a minimum variance sum for each class and indicates that features in the same class are more consistent. We divided the value of *SMI<sup>i</sup>* into six classes: the middle two classes were balanced, and the absolute value of the two classes was less than 1.5. If the absolute value of *SMI<sup>i</sup>* was more than 1.5, it showed that the relationship between the number of flash floods in two different time periods was unbalanced in city *i* [41].

#### (3) Standard deviational ellipse

The standard deviational ellipse (SDE) has long served as a general geographic information system tool used to measure bivariate distributed characteristics. The tool typically is used to delineate the geographic distribution trend of features by summarizing both their orientation and dispersion. Since our flash flood data is presented in the form of points, this method can be used to determine the direction and trend. In ArcGIS10.2, the SDE is primarily determined by three elements: average location, dispersion (or concentration), and orientation. In addition, the SDE can be described as one, two, or three standard deviations, which can contain approximately 68%, 95%, or 99% of centroids of all input features, respectively. In this study, we selected one standard deviation [42].

#### (4) Spatial gravity center model

The spatial gravity center model has the advantage to research the spatial-temporal migrations of factors by analyzing the trajectory of their gravity center. We used the spatial gravity center model visually and accurately to reveal the distribution and evolution characteristics of factors in two-dimensional space [40]. To analyze the change trajectories of flash floods, precipitation, and human activities, we calculated the gravity center coordinates of the flash floods, annual mean precipitation, and population density [43]. The time interval of annual mean precipitation and population data was from 2001 to 2015, and we analyzed flash floods consistent with this interval. The gravity center coordinate of the flash floods is given as follows:

$$\mathcal{G}\_f(\mathbf{x}) = \frac{\sum\_{i=1}^n f\_i(\mathbf{x})}{n}, \mathcal{G}\_f(y) = \frac{\sum\_{i=1}^n f\_i(y)}{n} \tag{3}$$

where *G<sup>f</sup>* (*x*) and *G<sup>f</sup>* (*y*) show the gravity center coordinate of annual flash floods, *n* is the annual number of flash floods, and *f<sup>i</sup>* (*x*) and *f<sup>i</sup>* (*y*) are the geometric coordinates of *i*-th flash floods (*i* = 1, 2,· · · *n*) [25]. Moreover, the gravity center coordinate of the annual mean precipitation and population density are given as follows:

$$\mathbf{G}(\mathbf{x}) = \frac{\sum\_{i=1}^{n} \mathbf{x}\_{i} \times k\_{i}}{\sum\_{i=1}^{n} k\_{i}}, \mathbf{G}(\mathbf{y}) = \frac{\sum\_{i=1}^{n} y\_{i} \times k\_{i}}{\sum\_{i=1}^{n} k\_{i}} \tag{4}$$

where *G*(*x*) and *G*(*y*) express the yearly gravity center coordinate of the factor (annual mean precipitation or population density), (*x<sup>i</sup>* , *y<sup>i</sup>* ) is the geometric coordinate of *i*-th meteorological station of annual mean precipitation (or municipal administrative unit of population density), and *k<sup>i</sup>* refers to the attribute value of the *i*-th meteorological station (or municipal administrative unit) [40].

#### 2.3.3. Driving Force Analysis

In this study, we explored the relationship between flash floods and driving factors in subregions of the landcover. These subregions include grassland, settlement, farmland, and forest, as almost all flash floods occurred in these subregions. We generated 1000 random points in each subregion and extracted the values of the driving factors and the results of kernel density estimation for the flash floods at each random point on the spatiotemporal scale. On this basis, correlation and interaction were analyzed.

#### (1) Pearson correlation coefficient

The Pearson correlation coefficient is a classic mathematical method used to show the correlation between two factors *x* and *y* where the value of it ranges between (−1) and (+1). The mathematical formula is given by the following:

$$\tau = \frac{\sum\_{i=1}^{n} \mathbf{x}\_i y\_i - \frac{\sum\_{i=1}^{n} \mathbf{x}\_i \sum\_{i=1}^{n} y\_i}{n}}{\sqrt{\left(\sum\_{i=1}^{n} \mathbf{x}\_i^2 - \frac{\left(\sum\_{i=1}^{n} \mathbf{x}\_i\right)^2}{n}\right) \left(\sum\_{i=1}^{n} y\_i^2 - \frac{\left(\sum\_{i=1}^{n} y\_i\right)^2}{n}\right)}}\tag{5}$$

where *r* is the Pearson correlation coefficient between values *x* and *y*, and *n* refers to the numbers of values *x* and *y*. The *r* values and corresponding correlation levels are shown in Table 2 [44].


**Table 2.** Pearson correlation coefficient and corresponding correlation levels.

#### (2) Driving factors interaction on the flash floods

Different factors have different effects on the flash floods, and the same factors have different influence on the flash floods in the different subregions of the landcover. In this paper, many factors were selected to explore the driving force, there may be a correlation between the factors. To avoid the multicollinearity of driving factors and explore the interaction of driving factors on flash floods and understand which factors were dominant in the interaction, we selected principal component analysis and multiple linear regression, which enabled us to summarize and visualize the information in the driving factors.

Principal component analysis is an oldest multivariate technique and it is employed by almost all scientific disciplines. Its goal is to reflect the important information from the original data. Meanwhile, it can transform the multicollinearity of driving factors into a set of linearly independent principal

components [45]. Detailed information about the principal component analysis were described by previous researches. We determined the number of principal components by the total variance, which was more than 85% [46]. In addition, we measured the contribution of the variable on the principal component by using the "FactoMineR" R package.

Multiple linear regression model is a statistical tool that can be considered as the course of fitting models to data. It can summarize data as well as investigate the relationship between input variables. In this study, the input variables were the principal components of the output of the principal component analysis. Multivariate linear regression is described in detail in reference to previously published studies [47].

#### 2.3.4. Sensitivity analysis

To assess response of flash floods on economic development, we employed a sensitivity assessment model to calculate the flash floods' sensitivity to GDP. This method is a quantitative analysis that researches the impacts of changing GDP on the flash floods. The formula is given as follows:

$$S = \frac{\left[\left(F\_{t\_2} - F\_{t\_1}\right) / F\_{t\_1}\right]}{\left[\left(G\_{t\_2} - G\_{t\_1}\right) / G\_{t\_1}\right]}\tag{6}$$

where *S* represents the value of sensitivity; *Ft*<sup>1</sup> and *Ft*<sup>2</sup> refer to, respectively, the flash floods at the start and end of the time period; and *Gt*<sup>1</sup> and *Gt*<sup>2</sup> refer to, respectively, GDP at the start and end of the time period. We divided sensitivity into four levels according to the published studies (Table 3) [40,48].


**Table 3.** *S* value and corresponding sensitivity level.

#### **3. Results**

#### *3.1. Temporal Pattern of the Flash Floods*

Figure 2 shows the characteristics of the temporal variation of flash floods in Yunnan. The annual flash floods gradually increased from 1949 to 2015 (Figure 2b, Table 4). On the basis of the descriptions in Section 2.3.1, annual flash floods were divided into four time periods, the number of flash floods was 104, 331, 704, and 2027 during 1949–1962, 1963–1981, 1982–1995, and 1996–2015, respectively (Figure 2a). For the four time periods (1949–1962, 1963–1981, 1982–1995, and 1996–2015), a high level of monthly flash floods occurred in June (30, 53, 133, and 297 flash floods, respectively), July (31, 99, 213, and 643 flash floods, respectively), and August (34, 94, 131, and 552 flash floods, respectively), and no flash floods occurred in February (Figure 2c).

respectively), July (31, 99, 213, and 643 flash floods, respectively), and August (34, 94, 131, and 552

**Table 4.** The number of flash floods on different time scales. **Year Interval Year June July August**  1949–1962 104 30 31 34 1963–1981 331 53 99 94 1982–1995 704 133 213 131 1996–2015 2027 297 643 552

flash floods, respectively), and no flash floods occurred in February (Figure 2c).

**Figure 2.** The characteristics of temporal variation of the flash floods: (**a**) a histogram of the number of the flash floods per year and the year interval of the flash floods based on changepoint analysis (the green dotted line is 1949–1962, the blue dotted line is 1963–1981, the purple dotted line is 1982– 1995, and the red dotted line is 1996–2015); (**b**) variation trends of annual flash floods. The red line is the fitting line and the dark green line is the change line of the annual number of flash floods; and(**c**) **Figure 2.** The characteristics of temporal variation of the flash floods: (**a**) a histogram of the number of the flash floods per year and the year interval of the flash floods based on changepoint analysis (the green dotted line is 1949–1962, the blue dotted line is 1963–1981, the purple dotted line is 1982–1995, and the red dotted line is 1996–2015); (**b**) variation trends of annual flash floods. The red line is the fitting line and the dark green line is the change line of the annual number of flash floods; and (**c**) characteristics of monthly flash floods in different time periods.


characteristics of monthly flash floods in different time periods. **Table 4.** The number of flash floods on different time scales.

#### Baoshan (10 flash floods), Yuxi (10 flash floods), and Zhaotong (10 flash floods), and the lowest level occurred in Lijiang in 1949–1962 (Figure 3a). In the 1963–1981 period, the most frequent occurrence *3.2. Spatial Pattern of the Flash Floods*

#### of flash floods was in Baoshan (47 flash floods); other high-incidence areas included Kunming (32 flash floods), Dali (37 flash floods), and Yuxi (32 flash floods) (Figure 3b). Furthermore, the 3.2.1. The Result of Kernel Density Estimation

frequency of the flash floods has increased significantly since the 1982–1995 period. A high frequency of flash floods occurred in Qujing (113 flash floods), Dali (88 flash floods), Chuxiong (74 flash floods), and Baoshan (76 flash floods) in 1982–1995; a low frequency was concentrated in Nujiang (7 flash floods) and Xishuangbanna (6 flash floods) (Figure 3c). In general, the number of the flash floods in Yunnan reached its maximum in the 1996–2015 period. The areas with more than 200 flash floods included Qujing (275 flash floods) and Yuxi (201 flash floods), and the lowest number occurred in Xishuangbanna (30 flash floods) (Figure 3d). The results of kernel density estimations of flash floods are shown in Figure 3. A relatively high number of flash floods was concentrated in Kunming (18 flash floods), Chuxiong (14 flash floods), Baoshan (10 flash floods), Yuxi (10 flash floods), and Zhaotong (10 flash floods), and the lowest leveloccurred in Lijiang in 1949–1962 (Figure 3a). In the 1963–1981 period, the most frequent occurrence of flash floods was in Baoshan (47 flash floods); other high-incidence areas included Kunming (32 flash floods), Dali (37 flash floods), and Yuxi (32 flash floods) (Figure 3b). Furthermore, the frequency of the flash floods has increased significantly since the 1982–1995 period. A high frequency of flash floods occurred in Qujing (113 flash floods), Dali (88 flash floods), Chuxiong (74 flash floods), and Baoshan (76 flash floods) in 1982–1995; a low frequency was concentrated in Nujiang (7 flash floods) and Xishuangbanna (6 flash floods) (Figure 3c). In general, the number of the flash floods in Yunnan reached its maximum in the 1996–2015 period. The areas with more than 200 flash floods included Qujing (275 flash floods) and Yuxi (201 flash floods), and the lowest number occurred in Xishuangbanna (30 flash floods) (Figure 3d).

**Figure 3.** Kernel density estimation of the flash floods for the four time periods: (**a**) 1949–1962, (**b**) **Figure 3.** Kernel density estimation of the flash floods for the four time periods: (**a**) 1949–1962, (**b**) 1963–1981, (**c**) 1982–1995, and (**d**) 1996–2015.

#### 1963–1981, (**c**) 1982–1995, and (**d**) 1996–2015. 3.2.2. Results of Spatial Mismatch Analysis and SDE

3.2.2. Results of Spatial Mismatch Analysis and SDE The regions with spatial unbalance were distributed mainly in Zhaotong, Qujing, Kunming, Chuxiong, Puer, Dali, Diqing, and Baoshan from the 1949–1962 to the 1963–1981 time period (Figure 4a). Similarly, standard deviational ellipses showed that the orientation and trends were located in these regions. From the 1963–1981 to the 1982–1995 time periods, the regions with an unbalanced frequency of flash floods had extended to the southern areas, which included Lincang and Xishuangbanna (Figure 4b). Additionally, the orientation and trend of standard deviational The regions with spatial unbalance were distributed mainly in Zhaotong, Qujing, Kunming, Chuxiong, Puer, Dali, Diqing, and Baoshan from the 1949–1962 to the 1963–1981 time period (Figure 4a). Similarly, standard deviational ellipses showed that the orientation and trends were located in these regions. From the 1963–1981 to the 1982–1995 time periods, the regions with an unbalanced frequency of flash floods had extended to the southern areas, which included Lincang and Xishuangbanna (Figure 4b). Additionally, the orientation and trend of standard deviational ellipses also were located in these areas. Fewer unbalanced areas, however, were evident from the 1982–1995 to the 1996–2015 time periods (Figure 4c), and the flash floods mainly occurred in these unbalanced areas (Zhaotong, Qujing, Kunming, Yuxi, Dali, Nujiang, and Baoshan). Overall, the orientation and trend of standard deviational ellipses were consistent with the unbalanced areas.

ellipses also were located in these areas. Fewer unbalanced areas, however, were evident from the 1982–1995 to the 1996–2015 time periods (Figure 4c), and the flash floods mainly occurred in these unbalanced areas (Zhaotong, Qujing, Kunming, Yuxi, Dali, Nujiang, and Baoshan). Overall, the orientation and trend of standard deviational ellipses were consistent with the unbalanced areas.

orientation and trend of standard deviational ellipses were consistent with the unbalanced areas.

**Figure 3.** Kernel density estimation of the flash floods for the four time periods: (**a**) 1949–1962, (**b**)

The regions with spatial unbalance were distributed mainly in Zhaotong, Qujing, Kunming, Chuxiong, Puer, Dali, Diqing, and Baoshan from the 1949–1962 to the 1963–1981 time period (Figure 4a). Similarly, standard deviational ellipses showed that the orientation and trends were located in these regions. From the 1963–1981 to the 1982–1995 time periods, the regions with an unbalanced frequency of flash floods had extended to the southern areas, which included Lincang and Xishuangbanna (Figure 4b). Additionally, the orientation and trend of standard deviational ellipses also were located in these areas. Fewer unbalanced areas, however, were evident from the 1982–1995 to the 1996–2015 time periods (Figure 4c), and the flash floods mainly occurred in these

**Figure 4.** The spatial pattern of spatial mismatch index and standard deviational ellipse at the start and end time periods: (**a**) from the 1949–1962 to the 1963–1981 time period, (**b**) from the 1963–1981 to the 1982–1995 time period, and (**c**) from the 1982–1995 to the 1996–2015 time period. Green dots and standard deviational ellipses indicate the start time period, and red indicates the end time period. *Sustainability* **2019**, *11*, x FOR PEER REVIEW 10 of 18 **Figure 4.** The spatial pattern of spatial mismatch index and standard deviational ellipse at the start and end time periods: (**a**) from the 1949–1962 to the 1963–1981 time period, (**b**) from the 1963–1981 to the 1982–1995 time period, and (**c**) from the 1982–1995 to the 1996–2015 time period. Green dots and

#### 3.2.3. Results of the Spatial Gravity Center Model standard deviational ellipses indicate the start time period, and red indicates the end time period.

gradually along the southwest region from 2001 to 2015.

1963–1981, (**c**) 1982–1995, and (**d**) 1996–2015.

3.2.2. Results of Spatial Mismatch Analysis and SDE

As shown in Figure 5, the gravity center of the flash floods was located mainly in Chuxiong, and its change trajectories were random. The gravity center of annual mean precipitation was focused on the border between Chuxiong and Puer, and its change trajectories were also random, but they had some similarity to that of the flash floods. The gravity center of the population moved gradually along the southwest region from 2001 to 2015. 3.2.3. Results of the Spatial Gravity Center Model As shown in Figure 5, the gravity center of the flash floods was located mainly in Chuxiong, and its change trajectories were random. The gravity center of annual mean precipitation was focused on the border between Chuxiong and Puer, and its change trajectories were also random, but they had some similarity to that of the flash floods. The gravity center of the population moved

**Figure 5.** Change trajectories of gravity centers of flash floods, annual mean precipitation, and population from 2001 to 2015. **Figure 5.** Change trajectories of gravity centers of flash floods, annual mean precipitation, and population from 2001 to 2015.

#### *3.3. Driving Factors for the Spatial Distribution of the Flash Floods 3.3. Driving Factors for the Spatial Distribution of the Flash Floods*

We performed a correlation analysis between the flash floods and driving factors in the different subregions of the landcover, as shown in Table 5. Additionally, we analyzed the interaction of driving factors on the flash floods; the results are presented in Figure 6. In the grassland, the highest *r* value was the H24\_20 (*r* = 0.501, *P* < 0.001). Other higher *r* values included M10\_20 (*r* = 0.487, *P* < 0.001), H6\_20 (*r* = 0.449, *P* < 0.001), ELE (*r* = 0.431, *P* < 0.001), and M60\_20 (*r* = 0.335, *P* = 0.001). The highest R2 value of multiple linear regression was 0.213, which was based on the principal component (Dim.1, Dim.2, Dim.3, and Dim.4). Driving factors that had a greater We performed a correlation analysis between the flash floods and driving factors in the different subregions of the landcover, as shown in Table 5. Additionally, we analyzed the interaction of driving factors on the flash floods; the results are presented in Figure 6. In the grassland, the highest *r* value was the H24\_20 (*r* = 0.501, *P* < 0.001). Other higher *r* values included M10\_20 (*r* = 0.487, *P* < 0.001), H6\_20 (*r* = 0.449, *P* < 0.001), ELE (*r* = 0.431, *P* < 0.001), and M60\_20 (*r* = 0.335, *P* = 0.001). The highest R <sup>2</sup> value of multiple linear regression was 0.213, which was based on the principal component (Dim.1,

(16.84%), H6\_20 (15.21%), ELE (12.73%), and PD (10.49%). Regarding the farmland, M10\_20, H6\_20, ELE, H24\_20, and M60\_20 were the most important driving factors, with *r* values of 0.445 (*P* < 0.001), 0.445 (*P* < 0.001), 0.402 (*P* < 0.001), 0.381 (*P* < 0.001), and 0.348 (*P* = 0.001), respectively. The highest R2 value occurred in Dim.1, and the main contributing factors were M10\_20 (23.01%), M60\_20 (21.81%), H6\_20 (21.07%), H24\_20 (21.06%), and ELE (12.28%). The characteristics of forest were

contribution included M10\_20 (17.91%), M60\_20 (17.39%), H24\_20 (16.99%), and H6\_20 (16.93%). Regarding the settlement, the higher *r* values of driving factors exhibited the following ranking: Dim.2, Dim.3, and Dim.4). Driving factors that had a greater contribution included M10\_20 (17.91%), M60\_20 (17.39%), H24\_20 (16.99%), and H6\_20 (16.93%). Regarding the settlement, the higher *r* values of driving factors exhibited the following ranking: M10\_20 (*r* = 0.675, *P* < 0.001) > ELE (*r* = 0.674, *P* < 0.001) > M60\_20 (*r* = 0.593, *P* < 0.001) > H24\_20 (*r* = 0.519, *P* < 0.001) > H6\_20 (*r* = 0.395, *P* < 0.001). The interaction of Dim.1 and Dim.4 contributed the highest R<sup>2</sup> value, which were controlled mainly by the M10\_20 (17.95%), M60\_20 (17.79%), H24\_20 (16.84%), H6\_20 (15.21%), ELE (12.73%), and PD (10.49%). Regarding the farmland, M10\_20, H6\_20, ELE, H24\_20, and M60\_20 were the most important driving factors, with *r* values of 0.445 (*P* < 0.001), 0.445 (*P* < 0.001), 0.402 (*P* < 0.001), 0.381 (*P* < 0.001), and 0.348 (*P* = 0.001), respectively. The highest R<sup>2</sup> value occurred in Dim.1, and the main contributing factors were M10\_20 (23.01%), M60\_20 (21.81%), H6\_20 (21.07%), H24\_20 (21.06%), and ELE (12.28%). The characteristics of forest were similar to those of the other three subregions. The higher *r* values included H6\_20 (*r* = 0.492, *P* < 0.001), H24\_20 (*r* = 0.485, *P* < 0.001), M10\_20 (*r* = 0.466, *P* < 0.001), and M60\_20 (*r* = 0.326, *P* = 0.001). In addition, the highest R<sup>2</sup> was determined by the interaction of Dim.1 and Dim.3, and H6\_20 (17.14%), M10\_20 (16.83%), M60\_20 (16.19%), H24\_20 (15.72%), and ELE (10.48%) were dominant.

**Table 5.** Pearson correlation coefficient (*r*) between the flash floods and driving factors in the different subregions of the landcover based on Formula (5).


**Figure 6.** Driving factors interaction based on multiple linear regression and principal component analysis for flash floods, and the contribution of driving factors to the principal components (Dim.1, Dim.2, Dim.3, and Dim.4) in the different subregions of the landcover: (**a**) R2 value of multiple linear regression of principal components to the flash floods in grassland; (**b**) the contribution of driving factors to Dim.1 and Dim.3 in grassland; (**c**) R2 value of multiple linear regression of principal components to the flash floods in settlement; (**d**) the contribution of driving factors to Dim.1 and Dim.4 in settlement; (**e**) R2 value of multiple linear regression of principal components to the flash floods in farmland; (**f**) the contribution of driving factors to Dim.1 in farmland; (**g**) R2 value of multiple linear regression of principal components to the flash floods in forest; and (**h**) the contribution of driving factors to Dim.1 and Dim.3 in forest. The red number is the highest R2 value. The contribution of driving factors to the principal components greater than the red dotted line **Figure 6.** Driving factors interaction based on multiple linear regression and principal component analysis for flash floods, and the contribution of driving factors to the principal components (Dim.1, Dim.2, Dim.3, and Dim.4) in the different subregions of the landcover: (**a**) R<sup>2</sup> value of multiple linear regression of principal components to the flash floods in grassland; (**b**) the contribution of driving factors to Dim.1 and Dim.3 in grassland; (**c**) R<sup>2</sup> value of multiple linear regression of principal components to the flash floods in settlement; (**d**) the contribution of driving factors to Dim.1 and Dim.4 in settlement; (**e**) R<sup>2</sup> value of multiple linear regression of principal components to the flash floods in farmland; (**f**) the contribution of driving factors to Dim.1 in farmland; (**g**) R<sup>2</sup> value of multiple linear regression of principal components to the flash floods in forest; and (**h**) the contribution of driving factors to Dim.1 and Dim.3 in forest. The red number is the highest R<sup>2</sup> value. The contribution of driving factors to the principal components greater than the red dotted line indicates that they are dominant.

**Factors Grassland Settlement Farmland Forest** 

*3.4. Sensitivity Analysis between the Flash Floods and Economy Development* 

M10\_20 0.487 <0.001 0.675 <0.001 0.445 <0.001 0.466 <0.001 M60\_20 0.335 0.001 0.593 <0.001 0.348 0.001 0.326 0.001 H6\_20 0.449 <0.001 0.395 <0.001 0.445 <0.001 0.492 <0.001 H24\_20 0.501 <0.001 0.519 <0.001 0.381 <0.001 0.485 <0.001 ELE 0.431 <0.001 0.674 <0.001 0.402 <0.001 0.257 0.01 TR −0.077 0.446 −0.146 0.172 0.219 0.032 −0.014 0.888 SLP −0.05 0.619 −0.094 0.382 −0.176 0.085 −0.081 0.424 NDVI −0.241 0.016 0.061 0.571 −0.222 0.029 −0.234 0.02 PD 0.082 0.42 −0.211 0.048 0.108 0.297 −0.098 0.335 GDP 0.098 0.332 0.042 0.697 0.226 0.027 0.233 0.02

By combining the data of the flash floods and GDP and using Formula (6), we calculated the value of sensitivity (*S*) of the flash floods to the economic development of each city in Yunnan Province, as shown in Figure 7. From an overall perspective, fewer regions experienced medium and high sensitivity during the study period, and the quantity of regions without sensitivity first decreased and then remained stable. During 1995–2000, all regions were non-sensitive. In comparison, the quantity of low-sensitivity regions during 2000–2005 and 2005–2010 increased to

*r P r P r P r P* 

indicates that they are dominant.
