# Time-Series Variation of Landslide Expansion in Areas with a Low Frequency of Heavy Rainfall

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Site

^{2}(Figure 1). The elevation of the area ranges from 145 to 1317 m above sea level. The average slope gradient calculated from the 10 m DEM was 28.5°. The study area is in the Kamuikotan Zone and consists primarily of Late Cretaceous sedimentary rocks (sandstone, siltstone, and mudstone) (16 km

^{2}) and basalt blocks, which are accretionary complexes from the Late Jurassic–Early Cretaceous (35 km

^{2}) [25]. The vegetation in the study area has been partially transformed into an afforestation site for Abies sachalinensis and Larix kaempferi, but most of the vegetation is covered with a natural mixed coniferous forest [26].

## 3. Methods

#### 3.1. Data

#### 3.2. Interpretation and Classification of Landslides and Calculation of Individual Landslide Areas

#### 3.3. Flow of the Analysis

^{2}, 250–500 m

^{2}, 500–750 m

^{2}, 750–1000 m

^{2}, and >1000 m

^{2}).

## 4. Results

#### 4.1. Area Frequency Distribution and Density of Original Landslides

^{2}(Figure 7).

^{2}had a landslide density of 59%, accounting for more than half of the total; moreover, the maximum landslide area was 6312 m

^{2}(Figure 7a). The total number of landslides in 1993 was 108, and the landslide area of 0–500 m

^{2}had a landslide density of 56%, accounting for more than half of the total, with a maximum landslide area of 3419 m

^{2}(Figure 7b). The total number of landslides in 2003 was 383, which was the largest number during the analysis period, and the landslide density in the section from 0–1000 m

^{2}accounted for more than half of the total (70%). The maximum landslide area was 11,466 m

^{2}, which was the largest during the analysis period (Figure 7c). The number of landslides in 2008 was 13, which was the third lowest during the analysis period, and the landslide area of 0–1000 m

^{2}had a landslide density of 77%, accounting for more than half of the total. The maximum landslide area was 2790 m

^{2}(Figure 7d).

#### 4.2. Area of Expansion and Original Landslides and Transition in Their Ratios

^{2}/year), excluding the period from 1993 to 2003 (heavy rainfall was recorded in 2003) (Figure 8a). The ATOL ranged from 488 (m

^{2}/year) (1974–1983) to 7828 (m

^{2}/year) (1983–1993), a difference of approximately 16-fold. In addition, the ATOL was 39,708 (m

^{2}/year) during the period from 1993 to 2003, including 2003, when heavy rainfall was recorded.

^{2}/year). The period with the largest ATEL was from 2003 to 2008, recorded after the heavy rain in 2003 (6681 (m

^{2}/year). The average ATEL, excluding the period from 2003 to 2008, was 1181 (m

^{2}/year). Therefore, the ATEL from 2003 to 2008 was approximately six-fold that of the average ATEL, excluding the period from 2003 to 2008.

^{2}/year)) was smaller than the ATOL from 1993 to 2003 (including the heavy rainfall in 2003) and from 1983 to 1993 by 0.17-fold and 0.85-fold, respectively. However, it was 2.17-fold higher than the ATOL (3075 (m

^{2}/year)) during the analysis period (1963–2013), excluding 1993–2003, which recorded the heavy rainfall in 2003. Furthermore, the ATEL from 2003 to 2008 was also higher than the ATOL from 1963 to 1974 (1.82-fold), 1974 to 1983 (13.7-fold), and 2008 to 2013 (6.68-fold), respectively. Furthermore, the ATEL (2988 (m

^{2}/year)) in the period from 2008 to 2013 was smaller than the ATOL in the period from 1993 to 2003 (including the heavy rainfalls in 2003) (0.08-fold), 1983 to 1993 (0.38-fold), and 1963 to 1974 (0.82-fold). However, it remained relatively consistent with the ATOL (3075 (m

^{2}/year)) during the analysis period (1963–2013), excluding the 1993–2003 period, which featured heavy rainfall in 2003 (0.97-fold).

#### 4.3. Relationship between the Ratio of Expanding and Original Landslide Areas and the Number of Remaining Landslides

^{2}) in 1983–1993 and the highest at 8.76 (/km

^{2}) in 2003–2008 (Figure 8b). The average number of remaining landslides over the entire period was 4.11 (/km

^{2}). From 1983 to 1993, when the ATEL-to-ATOL ratio was the lowest, the number of remaining landslides was also the lowest. However, the number of remaining landslides during the period when the ATEL-to-ATOL ratio exceeded 1 (2003–2008 and 2008–2013) was within the top two in the analysis period. In addition, the period in which the ATEL-to-ATOL ratio was the third largest (1963–1974) corresponded to the period in which the number of remaining landslides was the third largest. Therefore, a corresponding relationship was observed between the ATEL-to-ATOL ratio and the number of remaining landslides.

#### 4.4. Relationship between Transitions in Expanding Landslides, Elapsed Time since the Landslide, and Rainfall Intensity

^{2}= 0.33 (Figure 10a). Regarding the relationship between the RNEL and maximum daily rainfall during the longest period after the landslide in the analysis period (over 29 years after the landslide), the RNEL increased with rainfall intensity. For the relationship between the RNEL and the maximum daily rainfall 9–10 years after the landslide, the RNEL, with a maximum daily rainfall of 388 mm, was similar to or greater than the RNEL with a maximum daily rainfall of 131 mm. In addition, the analysis of the relationship between the RNEL and the period after the landslide when the maximum daily rainfall was the highest showed that the RNEL was 22% for the period 9–10 years after the landslide and 75% for the period beyond 29 years after the landslide. This indicated that the RNEL value for the period beyond 29 years after the landslide exceeded that for 9–10 years after the landslide. In addition, the RNEL value at >29 years after the landslide was the highest during the entire analysis period. Therefore, the RNEL increased with the rainfall intensity of the maximum daily rainfall, regardless of the time that had elapsed after the landslide.

^{2}= 0.64 (Figure 10b)). An analysis of the relationship between the RELA and maximum daily rainfall during the longest period after the landslide in the analysis period (29 years after the landslide) showed that the RELA value increased as the rainfall intensity increased. Moreover, an analysis of the relationship between the RELA and maximum daily rainfall 9–10 years after the landslide showed that the RELA with a maximum daily rainfall of 388 mm was greater than the RELA with a maximum daily rainfall of 131 mm. In addition, an analysis of the relationship between the RELA and the period after the landslide showed that when the maximum daily rainfall was the highest (maximum daily rainfall: 388 mm), the RELA was 18% for the period 9–10 years after the landslide and 27% for the period more than 29 years after the landslide. Therefore, the RELA at >29 years after the landslide exceeded the RELA at 9–10 years after the landslide. As mentioned earlier, the RELA also increased with the rainfall intensity of the maximum daily rainfall, regardless of the elapsed time after the landslide, as was similar for the RNEL.

#### 4.5. Transition of the Number and Area of Remaining Landslides after the Landslide, Relationship between the Original Landslide Area and the Number of Remaining Landslides

^{t}(R

^{2}= 0.79)). The transition of the RNRL for each period reached the highest in the period immediately after the landslide (approximately 5–20 years after the landslide) and then decreased monotonically in each period; however, the reduction rate varied depending on the period. In 1974, the RNRL reached 18% in the period 9–20 years immediately after the landslide and then decreased in the period 39–50 years after the landslide. The reduction rate of the RNRL in 1974 was −0.5 (Figure 11a). In 1993, the RNRL reached 67% in the period 10–20 years after the landslide and then decreased in the period 20–30 years after the landslide. The reduction rate of the RNRL in 1993 was −4.5 (Figure 11a). In 2003, the RNRL reached 90% in the period 5–10 years after the landslide and then decreased in the period 10–20 years after the landslide. In 2003, the reduction rate of the RNRL was −5.7 (Figure 11a). In 1974, the smallest RNRL (18%) was observed immediately after the landslide, and the largest value was observed in 2003 (90%) (Figure 11a). The reduction rate of the RNRL was also the smallest in 1974 (−0.5) and largest in 2003 (−5.7).

^{−0.115t}(R

^{2}= 0.75)). The transition of the RRLA for each period was the highest in the period immediately after the landslide (approximately 5–20 years after the landslide); however, it then decreased monotonically in each period, although the reduction rate varied. In 1974, the RRLA reached 22% in the period 9–20 years immediately after the landslide and then decreased in the period 39–50 years after the landslide. The reduction rate of the RRLA in 1974 was −0.2 (Figure 11b). Excluding the huge landslide in 1974, the RRLA reached 9% in the period 9–20 years after the landslide and then decreased in the period 39–50 years after the landslide. In 1974, the reduction rate of the RRLA, with the exclusion of large-scale landslides, was −0.3 (Figure 11b). In 1993, the RRLA reached 39% in the period 10–20 years after the landslide and then decreased in the period 20–30 years after the landslide. The reduction rate of the RRLA in 1993 was −2.8 (Figure 11b). In 2003, the RRLA reached 47% in the period 5 to 10 years after the landslide and then decreased in the period 10 to 20 years after the landslide. The reduction rate of RRLA in 2003 was −5.7 (Figure 11b). The lowest and highest RRLA values immediately after the landslide were observed in 1974 (9%) and 2003 (47%), respectively (Figure 11b). The lowest and highest RRLA reduction rates were observed in 1974 (−0.2) and 2003 (−5.7).

^{2}, 250–500 m

^{2}, 500–750 m

^{2}, and 750–1000 m

^{2}. In contrast, 20% had an original landslide area of ≥1000 m

^{2}.

^{2}, the RNRL became 0% 30 years after the landslide, whereas when the original landslide area was in the range of 750–1000 m

^{2}, the RNRL remained at 25%, even 34 years after the landslide. Therefore, the larger the area of the original landslide, the easier it was for the landslide to persist.

## 5. Discussion

#### 5.1. Factors and Characteristics for the Transitioning of Expanding Landslide in Areas with a Low Frequency of Heavy Rainfall

#### 5.2. Ratio of Remaining Landslides to the Original Landslide over Time

^{t}. Tsukamoto et al. [14] investigated the transition of landslides over the 36-year period from 1959 to 1995 on the southeastern slope of Mt. South Kiso, Japan. They reported that 10 years after 1959, the RNRL landslide was at 41%. According to the estimation formula in this study (R(t) = 0.93

^{t}), the RNRL 10 years after the landslide was estimated to be 48%. Therefore, although the value estimated in this study was approximately 7% higher, the results were almost the same as those of Tsukamoto et al. [14]. In addition, Samia et al. [6] quantitatively investigated the duration of original landslides and the rate of remaining landslides over approximately 70 years in the Collazzone region of Umbria, central Italy. Samia et al. [6] calculated the remaining landslide rate as the product of the RNRL and the ratio of the remaining landslide area to the catchment area. Therefore, although slightly different from the estimation formula in this study, the remaining landslide rates for 10 and 40 years after the landslide were reported to be 25% and 1%, respectively. With the estimation formula used in this study, the RNRL was 48% at 10 years after the landslide, which was 23% higher than that reported by Samia et al. [6]. However, 40 years after the landslide, it was 5%, which was similar to that reported by Samia et al. [6]. Therefore, the estimation formula proposed in this study may show a deviation from the measured value for the duration immediately after the landslide. However, this deviation was considered to be negligible.

#### 5.3. Evaluation of the Influence Period of the Expanding Landslide, Considering the Transitioning of the Remaining Landslide

## 6. Conclusions

^{t}). Therefore, by multiplying the function for the maximum daily rainfall after a landslide by the estimation formula for the number of remaining landslides, we propose an empirical formula for the number of expanding landslides after heavy rainfall. Therefore, it is possible to evaluate the impact period of the expanding landslides caused by heavy rainfall in this area. Thus, it is predicted that after heavy rainfall, the number of remaining landslides will increase, and even after a certain amount of time has passed, once heavy rainfall occurs, expanding landslides will become active.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Classification of the original and expanding landslides using orthophotography. Original landslide: landslides where a bare area was observed during a set photography period (blue outline in the

**center**image), compared with the area covered by vegetation during the previous photography period (

**left**image). Expanding landslide: landslides where the bare area has expanded to the area (red outline in the

**right**image) adjacent to the landslide, compared with the previous photography period (

**center**image).

**Figure 4.**Extraction of remaining landslides (shrunk landslides). Remaining landslide: a landslide where a bare area was continuously observed during the current period of interest (yellow solid line in the

**right**image), compared with the landslide area during the previous period of interest (red solid line in the

**left**image and red dotted line in the

**right**image).

**Figure 7.**Histogram of the original landslide area for each year: (

**a**) 1974, (

**b**) 1993, (

**c**) 2003, and (

**d**) 2008.

**Figure 8.**(

**a**): Relationship between the average annual total area of original and expanding landslides and ATEL/ATOL for each period. (

**b**): Relationship between the number of remaining landslides and ATEL/ATOL for each period.

**Figure 9.**(

**a**): Relationship between the RNEL and the elapsed time since the original landslide. (

**b**): Relationship between the RELA and the elapsed time since the original landslide.

**Figure 10.**(

**a**): Relationship between the RNEL and maximum daily rainfall. (

**b**): Relationship between the RELA and maximum daily rainfall.

**Figure 11.**(

**a**): Relationship between the RNRL and the elapsed time since the original landslide. (

**b**): The relationship between the RRLA and the elapsed time since the original landslide.

**Figure 12.**Transitions of RNRL over time for various original landslide areas (

**a**): 0–250 m

^{2}, (

**b**): 250–500 m

^{2}, (

**c**): 500–750 m

^{2}, (

**d**): 750–1000 m

^{2}, (

**e**): over 1000 m

^{2}.

Year | Date | Scale |
---|---|---|

1963 | 30 May, 17 June, 19 June, 28 June | 1:20,000 |

1974 | 1 August | 1:20,000 |

1983 | 29 September, 8 October, 19 October, 21 October | 1:16,000 |

1993 | 6 July, 31 August, 2 September, 15 September, 17 September | 1:16,000 |

2003 | 16 September | 1:16,000 |

2008 | 6 August, 10 September | 1:16,000 |

2013 | 6 September, 13 September, 27 September | 1:16,000 |

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**MDPI and ACS Style**

Koshimizu, K.; Uchida, T.
Time-Series Variation of Landslide Expansion in Areas with a Low Frequency of Heavy Rainfall. *Geosciences* **2023**, *13*, 314.
https://doi.org/10.3390/geosciences13100314

**AMA Style**

Koshimizu K, Uchida T.
Time-Series Variation of Landslide Expansion in Areas with a Low Frequency of Heavy Rainfall. *Geosciences*. 2023; 13(10):314.
https://doi.org/10.3390/geosciences13100314

**Chicago/Turabian Style**

Koshimizu, Ken’ichi, and Taro Uchida.
2023. "Time-Series Variation of Landslide Expansion in Areas with a Low Frequency of Heavy Rainfall" *Geosciences* 13, no. 10: 314.
https://doi.org/10.3390/geosciences13100314