*4.2. Factor-by-Factor Allocation*

First, we assumed that each factor was normally distributed, and its average value and standard deviation were ascertained, using one standard deviation to determine its reduction range. In this way, the extreme value of each parameter had less influence when calculating the weight, as shown in Table 3.


**Table 3.** Average value and standard deviation of each factor.

According to Juang et al., to improve the learning rate and accuracy of a similar neural network, the inconsistency of the difference between the numerical ranges of the parameters should be calculated, as before analysis, the input parameters must be normalized to avoid

the problem of temporary instability of the network and difficulty in convergence [42]. Accordingly, this study utilized a modified version of the interval-mapping method in Juang et al.'s normalization formula, and the maximum and minimum values obtained were between 0.1 and 1. rameters should be calculated, as before analysis, the input parameters must be normalized to avoid the problem of temporary instability of the network and difficulty in convergence [42]. Accordingly, this study utilized a modified version of the interval-mapping method in Juang et al.'s normalization formula, and the maximum and minimum values rameters should be calculated, as before analysis, the input parameters must be normalized to avoid the problem of temporary instability of the network and difficulty in convergence [42]. Accordingly, this study utilized a modified version of the interval-mapping method in Juang et al.'s normalization formula, and the maximum and minimum values

Distance from the collapse (m) 654.2 388.7 285.5–1022.9 Protected address 91.1 130.1 0–221.1

Distance from the collapse (m) 654.2 388.7 285.5–1022.9 Protected address 91.1 130.1 0–221.1

According to Juang et al., to improve the learning rate and accuracy of a similar neural network, the inconsistency of the difference between the numerical ranges of the pa-

According to Juang et al., to improve the learning rate and accuracy of a similar neural network, the inconsistency of the difference between the numerical ranges of the pa-

$$\text{"\(\text{"X"} \\_\text{"norm"} \text{"} = \text{"} \(\text{"X} + \text{a"} \) \text{"} \,\text{"} \,\text{X}\_{\text{norm}} = (\text{X} + \text{a}) / \text{b} \tag{1}$$

Among them: Among them: Among them:

obtained were between 0.1 and 1.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 10 of 19

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 10 of 19

$$\text{"{a} = "{\text{(}\text{``X} \text{''} \\_\text{``max''} \text{''} \text{''} \text{''} \text{'10X''} \text{''} \text{~''} \text{'min''}\text{''}\text{''} \text{'} \text{'a} = (\text{X}\_{\text{max}} - 10\text{X}\_{\text{min}}) / 9 \tag{2}$$

$$\mathbf{b} = (\mathbf{X}\_{\text{max}} - \mathbf{X}\_{\text{min}})/0.9 \tag{3}$$

In the above three formulae, Xnorm is the normalized value; X is the actual input parameter value; Xmax is the maximum actual input parameter; Xmin is the minimum actual input parameter. In the above three formulae, Xnorm is the normalized value; X is the actual input parameter value; Xmax is the maximum actual input parameter; Xmin is the minimum actual input parameter. In the above three formulae, Xnorm is the normalized value; X is the actual input parameter value; Xmax is the maximum actual input parameter; Xmin is the minimum actual input parameter.

For ease of calculation, a full score was held to be 100 points. In this study, the maximum and minimum range of the interval mapping method (0.1–1) is multiplied by the overall AHP weight of each factor and then multiplied by 100 to obtain the factors' respective maximum and minimum ratio ranges, as shown in Table 4. Substituting the data of each factor into Equation (1), the calculation formula of each factor can be calculated, and the factor weight of each river terrace calculated. For ease of calculation, a full score was held to be 100 points. In this study, the maximum and minimum range of the interval mapping method (0.1–1) is multiplied by the overall AHP weight of each factor and then multiplied by 100 to obtain the factors' respective maximum and minimum ratio ranges, as shown in Table 4. Substituting the data of each factor into Equation (1), the calculation formula of each factor can be calculated, and the factor weight of each river terrace calculated. For ease of calculation, a full score was held to be 100 points. In this study, the maximum and minimum range of the interval mapping method (0.1–1) is multiplied by the overall AHP weight of each factor and then multiplied by 100 to obtain the factors' respective maximum and minimum ratio ranges, as shown in Table 4. Substituting the data of each factor into Equation (1), the calculation formula of each factor can be calculated, and the factor weight of each river terrace calculated.

earth-rock flows occur, along with the characteristics of Taiwan geology. Adopting a predetermined risk standard of geological lithology, this study divides such geology into three broad categories, based on the maximum, minimum and intermediate values. Among the preservation factors, traffic and farmland were deemed to be either "present" or "not present" and also allocated based on the minimum values. **Table 4.** Weight distribution of each factor. **Factors Maximum Weighting Minimum Weighting**  Latent susceptibility Minimum height ratio (m) 11.1 1.11 Attack shore length (m) 13.3 1.33 Distance from river (m) 10.1 1.01 Average slope (degrees) 11.0 1.1 Distance from fault (m) 3.4 0.34 earth-rock flows occur, along with the characteristics of Taiwan geology. Adopting a predetermined risk standard of geological lithology, this study divides such geology into three broad categories, based on the maximum, minimum and intermediate values. Among the preservation factors, traffic and farmland were deemed to be either "present" or "not present" and also allocated based on the minimum values. **Table 4.** Weight distribution of each factor. **Factors Maximum Weighting Minimum Weighting**  Latent susceptibility Minimum height ratio (m) 11.1 1.11 Attack shore length (m) 13.3 1.33 Distance from river (m) 10.1 1.01 Average slope (degrees) 11.0 1.1 Distance from fault (m) 3.4 0.34 **Factors Maximum Weighting Minimum Weighting** Latent susceptibility factors Minimum height ratio (m) 11.1 1.11 Attack shore length (m) 13.3 1.33 Distance from river (m) 10.1 1.01 Average slope (degrees) 11.0 1.1 Distance from fault (m) 3.4 0.34 Number of potential streams affected 8.3 0.83 Geology 12.1 1.21 Number of erosion ditches 17.2 1.72 Distance from the collapse (m) 13.4 1.34 Total 100 10 Preservation factors Protected address 59.9 5.99 Traffic 29.3 2.93 Farmland 10.9 1.09 Total 100 10

In its geological aspects, this research is based on the results of a survey by the Civil Engineering Research Institute of the Ministry of Construction of Japan regarding where In its geological aspects, this research is based on the results of a survey by the Civil Engineering Research Institute of the Ministry of Construction of Japan regarding where **Table 4.** Weight distribution of each factor.

factors Geology 12.1 1.21 Number of erosion ditches 17.2 1.72 Distance from the collapse (m) 13.4 1.34 Total 100 10 Preservation factors Protected address 59.9 5.99 Traffic 29.3 2.93 Farmland 10.9 1.09 factors Geology 12.1 1.21 Number of erosion ditches 17.2 1.72 Distance from the collapse (m) 13.4 1.34 Total 100 10 Preservation factors Protected address 59.9 5.99 Traffic 29.3 2.93 Farmland 10.9 1.09 In its geological aspects, this research is based on the results of a survey by the Civil Engineering Research Institute of the Ministry of Construction of Japan regarding where earth-rock flows occur, along with the characteristics of Taiwan geology. Adopting a predetermined risk standard of geological lithology, this study divides such geology into three broad categories, based on the maximum, minimum and intermediate values. Among the preservation factors, traffic and farmland were deemed to be either "present" or "not present" and also allocated based on the minimum values.

Number of potential streams affected 8.3 0.83

Number of potential streams affected 8.3 0.83

Total 100 10

Total 100 10

### **5. Discussion**

*5.1. Risk Assessment of River Terraces*

The evaluation results for each river terrace are shown in Table 5. The average value (57.70) and standard deviation (13.346) were calculated by statistical methods, with the average value as the center plus or minus one standard deviation. After adjusting with the concept of rounding to integers, the boundaries were 70, 55 and 40. Thus, risk was divided into four categories: high risk (70–100), medium–high risk (55–69), medium risk (41–54) and low risk (0–40). These categories are also presented in map form in Figure 4.

After the risk assessment, 8 of the 40 focal river terraces were deemed to be high risk, 14 at medium-high risk, another 14 at medium risk, and the remaining 4 at low risk.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 12 of 19

**Figure 4.** The distribution map of the danger degree of the river terrace. **Figure 4.** The distribution map of the danger degree of the river terrace.

After the risk assessment, 8 of the 40 focal river terraces were deemed to be high risk,

14 at medium-high risk, another 14 at medium risk, and the remaining 4 at low risk.

were: (1) unsupervised classification using the SPOT-3 satellite multi-spectral state (XS) image map of Chen Youlanxi in each period to determine changes in river-terrace area; (2) comparison of river terraces in various periods with satellite images and aerial photos;

*5.2. Verification* 


**Table 5.** Risk assessment of river terraces.

### *5.2. Verification*

Three comparison methods were used in this research to verify our approach. These were: (1) unsupervised classification using the SPOT-3 satellite multi-spectral state (XS) image map of Chen Youlanxi in each period to determine changes in river-terrace area; (2) comparison of river terraces in various periods with satellite images and aerial photos; (3) comparison of historical disaster data from the Chenyulan River, covering a total of 87 floods linked to 42 discrete weather events from August 1959 through October 2009 [43].

### *5.3. Historical Disaster Comparison*

### 5.3.1. Dangerous River Terraces

As noted above, eight river terraces were deemed high-risk by our approach because they scored above 70 points. This indicated that the frequency of disasters there is high, damage to buildings and crops is noteworthy, and the area affected is relatively large. From historical disaster data, it can be seen that debris flows struck these eight terraces at 1.36 times the average rate; dike destruction (by number of occurrences) and land loss (in

hectares) were both 5 times the average; houses totally destroyed, 4.44 times the average; damaged houses, 4.09 times the average; number of deaths, 2.74 times the average. 5.3.2. County Pit I

damaged houses, 4.09 times the average; number of deaths, 2.74 times the average.

(3) comparison of historical disaster data from the Chenyulan River, covering a total of 87 floods linked to 42 discrete weather events from August 1959 through October 2009 [43].

As noted above, eight river terraces were deemed high-risk by our approach because they scored above 70 points. This indicated that the frequency of disasters there is high, damage to buildings and crops is noteworthy, and the area affected is relatively large. From historical disaster data, it can be seen that debris flows struck these eight terraces at 1.36 times the average rate; dike destruction (by number of occurrences) and land loss (in hectares) were both 5 times the average; houses totally destroyed, 4.44 times the average;

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 13 of 19

### 5.3.2. County Pit I County Pit I is a high-risk river terrace located on the right bank of the lower reaches

*5.3. Historical Disaster Comparison*  5.3.1. Dangerous River Terraces

County Pit I is a high-risk river terrace located on the right bank of the lower reaches of Chenyulan River. Figure 5 was obtained by extracting and overlapping images from five periods and shows little change in this area before and after Typhoon Hebo, whereas after Typhoon Tochigi, a shrinking trend in its land area can be observed. After the 72nd flood, the terrace's area was obviously reduced, but after Typhoon Morakot five years later, it had increased. of Chenyulan River. Figure 5 was obtained by extracting and overlapping images from five periods and shows little change in this area before and after Typhoon Hebo, whereas after Typhoon Tochigi, a shrinking trend in its land area can be observed. After the 72nd flood, the terrace's area was obviously reduced, but after Typhoon Morakot five years later, it had increased.

**Figure 5. Figure 5.** Area changed to County Pit I across five flooding events. Area changed to County Pit I across five flooding events.

County Pit Terrace I was destroyed by Typhoon Mintouli in 2004, which in turn caused the embankment of Junkengxi Terrace I to be washed away. The disaster area was very large, as shown in aerial photographs obtained from the Fourth River Bureau, Water Resources Department, Ministry of Economic Affairs (Figures 6–9).

**Figure 6.** The County Pit embankment in 2003 (the year before it was destroyed). **Figure 6.** The County Pit embankment in 2003 (the year before it was destroyed). **Figure 6.** The County Pit embankment in 2003 (the year before it was destroyed). **Figure 6.** The County Pit embankment in 2003 (the year before it was destroyed).

Resources Department, Ministry of Economic Affairs (Figures 6–9).

Resources Department, Ministry of Economic Affairs (Figures 6–9).

Resources Department, Ministry of Economic Affairs (Figures 6–9).

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*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 14 of 19

County Pit Terrace I was destroyed by Typhoon Mintouli in 2004, which in turn caused the embankment of Junkengxi Terrace I to be washed away. The disaster area was very large, as shown in aerial photographs obtained from the Fourth River Bureau, Water

County Pit Terrace I was destroyed by Typhoon Mintouli in 2004, which in turn caused the embankment of Junkengxi Terrace I to be washed away. The disaster area was very large, as shown in aerial photographs obtained from the Fourth River Bureau, Water

County Pit Terrace I was destroyed by Typhoon Mintouli in 2004, which in turn caused the embankment of Junkengxi Terrace I to be washed away. The disaster area was very large, as shown in aerial photographs obtained from the Fourth River Bureau, Water

**Figure 7.** The former area of the County Pit embankment, marked in blue, in 2004. **Figure 7.** The former area of the County Pit embankment, marked in blue, in 2004. **Figure 7.** The former area of the County Pit embankment, marked in blue, in 2004. **Figure 7.** The former area of the County Pit embankment, marked in blue, in 2004.

**Figure 8.** The Shang'an embankment in 2003 (before its destruction). **Figure 8.** The Shang'an embankment in 2003 (before its destruction). **Figure 8.** The Shang'an embankment in 2003 (before its destruction). **Figure 8.** The Shang'an embankment in 2003 (before its destruction).

**Figure 9.** The former area of the Shang'an embankment, marked in blue, in 2004. **Figure 9.** The former area of the Shang'an embankment, marked in blue, in 2004. **Figure 9.** The former area of the Shang'an embankment, marked in blue, in 2004.

flood, but after Typhoon Morakot, it was significantly reduced.

#### 5.3.3. Toutunxi Terrace I 5.3.3. Toutunxi Terrace I 5.3.3. Toutunxi Terrace I

Toutunxi I is a medium–high-risk river terrace located on the right bank of the middle reaches of Heshe River. A schematic diagram of its changes, based on image extraction and overlap from five flooding events, is presented in Figure 10. It is obvious from Figure 10 that the area of the terrace was broadly unchanged after Typhoon Toraji and the 72nd Toutunxi I is a medium–high-risk river terrace located on the right bank of the middle reaches of Heshe River. A schematic diagram of its changes, based on image extraction and overlap from five flooding events, is presented in Figure 10. It is obvious from Figure 10 that the area of the terrace was broadly unchanged after Typhoon Toraji and the 72nd flood, but after Typhoon Morakot, it was significantly reduced. Toutunxi I is a medium–high-risk river terrace located on the right bank of the middle reaches of Heshe River. A schematic diagram of its changes, based on image extraction and overlap from five flooding events, is presented in Figure 10. It is obvious from Figure 10 that the area of the terrace was broadly unchanged after Typhoon Toraji and the 72nd flood, but after Typhoon Morakot, it was significantly reduced.

**Figure 10. Figure 10.** Area changed to Toutunxi Terrace I across five flooding events. Area changed to Toutunxi Terrace I across five flooding events.

**Figure 10.** Area changed to Toutunxi Terrace I across five flooding events.

During Typhoon Morakot in 1998, three large landslides in the upper reaches of Toutunxi Creek indirectly formed soil and rock flows, which caused both banks of the downstream terraces to be washed away. In a satellite image from before this disaster (Figure 11, left), the channel of the Toukeng River is not obvious, being then only 20–30 m wide, but one taken after it (Figure 11, right) shows the channel clearly, as it had widened to 120 m. Toutunxi Creek indirectly formed soil and rock flows, which caused both banks of the downstream terraces to be washed away. In a satellite image from before this disaster (Figure 11, left), the channel of the Toukeng River is not obvious, being then only 20–30 m wide, but one taken after it (Figure 11, right) shows the channel clearly, as it had widened to 120 m.

During Typhoon Morakot in 1998, three large landslides in the upper reaches of

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**Figure 11.** The confluence of Toutunxi Creek and the Toukeng River before and after Typhoon Morakot in 1998, with study area marked in red. **Figure 11.** The confluence of Toutunxi Creek and the Toukeng River before and after Typhoon Morakot in 1998, with study area marked in red.

### **6. Conclusions 6. Conclusions**

The latent-susceptibility factors selected in this study through the literature were the length of the attacking bank, distance from fault, distance from river course, number of potential debris flows, minimum specific height, average slope, geology, number of erosion ditches, distance to collapsed land, etc. The three preservation factors selected were The latent-susceptibility factors selected in this study through the literature were the length of the attacking bank, distance from fault, distance from river course, number of potential debris flows, minimum specific height, average slope, geology, number of erosion ditches, distance to collapsed land, etc. The three preservation factors selected were the preservation of households, transportation and farmland; the risk to particular river

the preservation of households, transportation and farmland; the risk to particular river

ditions, those affecting the front of the river terrace were considered more important than those affecting the river terrace itself or the area behind it. Additionally, the results indicated that the preservation of households was deemed more important than traffic or

terraces was established from the latent-susceptibility factors and preservation factors. The results of the AHP analysis indicated that, among the latent-susceptibility factor conditions, those affecting the front of the river terrace were considered more important than those affecting the river terrace itself or the area behind it. Additionally, the results indicated that the preservation of households was deemed more important than traffic or farmland factors. The research also established that, of the 40 focal river terraces, the highest-risk ones were County Pit Terrace, County Kengxi Terraces I and II, Xinyi Terrace, Patriotic Terrace, Eighteenth Terrace I, Rona Terrace II and Heshe Terrace. In this study, a potential factor assessment framework was established to examine whether the research results were contradictory by comparing SPOT satellite images and historical hazards. Unlike other risk assessments of riverine terraces [10,11], the current environmental conditions of riverine terraces can be used to assess the risk of disasters. This study's risk-level designation has important implications for both disaster prevention and the evacuation of local residents when disasters occur, and, if generally adopted, it should mitigate loss of life and property. However, this study was not without its limitations. Chief among these was that it relied on the 5m × 5m DTM of Taiwan surveyed and mapped by the Chengda Satellite Center in 2004 to conduct its river-terrace risk assessments and stability analyses. The use of a more recent DTM would undoubtedly increase the accuracy of the analysis results. Additionally, when conducting stability analysis, due to limited drilling data from the Chenyulan River Basin, such data from Toutunxi River Terrace I were used as a proxy for it. Thus, more geological data would, therefore, improve our approach's ability to identify potential river-terrace collapses.

**Author Contributions:** Conceptualization, J.-Y.L.; data curation, Y.-M.H.; writing—original draft, Y.-M.H.; writing—review and editing, J.-C.C.; supervision, J.-Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study is part of the research results of the Ministry of Science and Technology number NSC100-2218-E-005-001. I would like to thank the staff for their hard work during the planning period and to express their greatest gratitude to the National Science Council for their support research. Funding has enabled this study to be successfully completed.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** The authors declare no conflict of interest.

**Data Availability Statement:** The data presented in this study are available in the article.

**Acknowledgments:** We would like to thank the anonymous reviewers for their helpful suggestions and feedback.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

