# A Hybrid Physical and Maximum-Entropy Landslide Susceptibility Model

^{*}

## Abstract

**:**

## 1. Introduction

^{6}m

^{3}over an area of about 2.6 km

^{2}, killed 41 people [5,6]. In 2010, a large landslide along the Hunza River in Pakistan not only erased two villages, but additionally created a large dam resulting in a lake which flooded villages upstream and threatened flooding of habitat downstream [7]. The cumulative effect of small landslides can also be very destructive, particularly when large regions are affected by swarms of landslides. Thousands of landslides caused by an intense storm in January of 1982 resulted in the loss of life of 25 people in the San Francisco Bay area. Although most of these slides were not of large size, some of the scars can still be recognized on recent aerial photography.

## 2. Study Area

^{2}watershed of San Pedro Creek (Pacifica, CA, USA) has been the focus of numerous landslide and hydrological studies as a result of its steep hillslopes and hazardous conditions [27]. Steep hillslopes are common with more than ten per cent of slopes greater than 35° and a median slope at 10 m precision of 21°. The maximum elevation is along the southern boundary of the watershed, the 578-m North Peak of Montara Mountain, a mass of granodiorite on the Salinian block that is moving northwestward with the Pacific Plate (Figure 1). The dominant surficial geology derives from marine deposits accreted at a convergent plate boundary, divided by the right-lateral Pilarcitos Fault into Jurassic/Cretaceous Franciscan Assemblage of graywacke, melange, greenstone, limestone and serpentinite to the north; and Paleogene marine sedimentary rocks to the south, including extensive uplifted turbidite beds visible along coastal bluffs. Mollisols of varying thickness have developed on weathered bedrock, slopewash, ravine fill and colluvium [28,29].

## 3. Methodology

#### 3.1. Physically-Based Model

_{s}) and root cohesion (C

_{r}), soil thickness D, soil density ρ

_{s}, and gravity g.

_{w}/ρ

_{s}is the ratio of the density of water to soil density, and the ratio of the height of the saturated zone, D

_{w}, and D, is the relative wetness w = D

_{w}/D.

^{2}h

^{−1}) derived as the product of hydraulic conductivity and soil thickness, and provides spatial patterns of relative wetness. In SINMAP, together with an estimate of specific catchment area a = A/b, where A is contributing area for unit contour length b, slope and recharge (R) relative to transmissivity T, the relative wetness w is derived as:

#### 3.2. Maximum Entropy Model

^{2}Arno River basin in the Tuscany region of Italy. Felicísimo [39] compared logistic regression, the maximum entropy (MaxEnt) application of Phillips et al. [40], multiple adaptive regression splines (MARS), and classification and regression trees (CART) for modeling landslide susceptibility in a region of northern Spain; CART and MaxEnt performed best based upon area under the receiver operator characteristic curve (AUC).

#### 3.3. Hybrid Model

#### 3.4. Landslide Scar Data and Causal Factors

## 4. Results

## 5. Discussion and Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Surficial geology of San Pedro Creek watershed, after Pampeyan [30].

**Figure 3.**Major vegetation types in undeveloped areas, San Pedro Creek watershed, based upon field mapping in 2002.

**Figure 4.**Shallow landslides associated with impervious runoff in San Pedro Creek watershed. At left is the crest of a failure that occurred below Higgins Road in 2003; at right are older scars from the 1970’s below a dirt road above Picardo Ranch. (Photographs by Jerry Davis)

**Figure 5.**Hybrid model combining a physical infinite-slope model extended spatially via soil thickness and transmissivity using downslope accumulated flows (SINMAP) with a maximum entropy (MaxEnt) model. SINMAP runs in ArcGIS, and ArcGIS geoprocessing tools are used to generate slope, plan curvature, stream distance and trail/road distance. If slope is used instead of stability index, this produces a purely statistical maximum-entropy model.

**Figure 6.**Slope-Area Plot generated by SINMAP, with inventory landslides from all years plotted with boundary curves of stability index and saturation.

**Figure 7.**Locations where landslides were first visible in 1941, 1975 and 1983, plotted on SINMAP Stability Index.

**Figure 8.**Receiver operator curves (ROC) generated by MaxEnt for 1941, 1975, and 1983 landslides, from 10-fold replicate models. Receiving operator curves are shown as the total range of replicate curves, with the mean curve in red.

**Figure 9.**Variable contribution jackknife plots generated by MaxEnt for 1941, 1975, and 1983 landslides, from 10-fold replicate models. Jackknife plots provide the variable contributions from geology (geolreg), proximity to streams (nearstream), proximity to trails (neartr_), plan curvature (plancurv2), profile curvature (profcurv2), stability index (si_gt0), and vegetation (veg_).

**Figure 10.**Maps generated by MaxEnt for 1941, 1975, and 1983 landslides, from 10-fold replicate models.

**Table 1.**SINMAP inputs for transmissivity (T), recharge (R), cohesion (C), friction (φ), and density (ρ). Soil data from Natural Resources Conservation Service SSURGO data, modified with colluvium depths from [30].

Parent material | Soil depth (m) | Hydraulic conductivity (m h^{−1}) | T (m^{2} h^{−1}) | R (m h^{−1}) | T/R (m) | C | Φ (°) | Ρ (kg m^{−3}) |
---|---|---|---|---|---|---|---|---|

granitic | 1 | 0.10 | 0.1 | 0.0002–0.0042 | 24–500 | 0–0.25 | 30–45 | 2000 |

colluvium | 3 | 0.03 | 0.1 | 0.0002–0.0042 | 24–500 | 0–0.25 | 30–45 | 2000 |

Imagery Year | 1941 | 1955 | 1975 | 1983 | 1997 |
---|---|---|---|---|---|

n scars | 154 | 39 | 142 | 253 | 10 |

n SI < 1.0 | 91 | 24 | 91 | 197 | 6 |

% | 59% | 62% | 64% | 78% | 60% |

**Table 3.**Maxent results by year of shallow landslide scars from aerial photography, including overall and 10-fold replicate models. Variables were chosen based upon their contribution to one or more models, and correlated variables (SI and slope) were not used together. Variable contributions are given as percent contribution (%) and permutation importance (PI). Models are evaluated as AUC for a threshold-independent assessment; for a threshold-dependent evaluation, arithmetic means of the 10 p values use the maximum test sensitivity + specificity threshold from MaxEnt [40]. Lambdas for categorical variables are for unreplicated models using all data for training.

1941 | 1975 | 1983 | |||||
---|---|---|---|---|---|---|---|

using: | SI | slope | SI | slope | SI | slope | |

n | 132 | 154 | 132 | 141 | 226 | 252 | |

AUC (using all data) | 0.795 | 0.796 | 0.822 | 0.814 | 0.859 | 0.857 | |

AUC subsequent-year test data | 0.778 | 0.795 | 0.749 | 0.742 | 0.853 | 0.842 | |

subsequent test year | 1955 | 1983 | 1997 | ||||

n slides in test year | 31 | 39 | 226 | 253 | 9 | 10 | |

10-fold replicates: | |||||||

AUC with 10-fold replicates | 0.728 | 0.743 | 0.782 | 0.772 | 0.839 | 0.836 | |

AUC standard deviation | 0.044 | 0.041 | 0.058 | 0.040 | 0.026 | 0.024 | |

p: maximum test sensitivity + specificity | 0.004 | 0.041 | 0.001 | 0.000 | 0.000 | 0.000 | |

SINMAP stability index | %C | 48.1 | 35.3 | 48 | |||

PI | 50.2 | 49.7 | 57.4 | ||||

Slope (°) | %C | 59.1 | 41 | 37.5 | |||

PI | 59.3 | 49.2 | 46.4 | ||||

Plan curvature | %C | 9.6 | 13.4 | 6.4 | 7.4 | 15.3 | 19.6 |

PI | 9.4 | 15 | 3.9 | 6.6 | 13.9 | 18.8 | |

Profile curvature | %C | 6.7 | 2.3 | 1.5 | 1.1 | 2.2 | 1.7 |

PI | 10.1 | 4.8 | 4.2 | 3.1 | 5 | 2.7 | |

50-m trail buffer | %C | 0 | 0.3 | 22.5 | 16.8 | 0.1 | 0 |

PI | 0 | 0.2 | 14.9 | 16.4 | 0.1 | 0 | |

Vegetation | %C | 35 | 23.7 | 32.2 | 33.2 | 24.6 | 27 |

PI | 29.9 | 20 | 24.9 | 23.6 | 15.5 | 20.3 | |

0. Farmed (1941), Developed (1975 & 1983) λ | 0.0 | 0.00 | −1.93 | −2.14 | −0.02 | −0.42 | |

1. Grassland λ | 1.76 | 1.17 | 1.06 | 1.25 | |||

2. Scrublands λ | 0.54 | 1.43 | 1.39 | ||||

3. Forest λ | −0.01 | −0.56 | −0.34 | ||||

Geology | %C | 0.5 | 1.1 | 2.1 | 0.6 | 9.8 | 13.4 |

PI | 0.1 | 0.7 | 2.2 | 1.2 | 7.9 | 11.4 | |

1. Granitic λ | −0.22 | −0.40 | 0.0 | 0.0 | −1.10 | −1.03 | |

2. Sandstone λ | 0.03 | 0.15 | |||||

3. Colluvium λ | 0.03 | −0.33 | −0.02 | 0.54 | 0.58 |

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**MDPI and ACS Style**

Davis, J.; Blesius, L.
A Hybrid Physical and Maximum-Entropy Landslide Susceptibility Model. *Entropy* **2015**, *17*, 4271-4292.
https://doi.org/10.3390/e17064271

**AMA Style**

Davis J, Blesius L.
A Hybrid Physical and Maximum-Entropy Landslide Susceptibility Model. *Entropy*. 2015; 17(6):4271-4292.
https://doi.org/10.3390/e17064271

**Chicago/Turabian Style**

Davis, Jerry, and Leonhard Blesius.
2015. "A Hybrid Physical and Maximum-Entropy Landslide Susceptibility Model" *Entropy* 17, no. 6: 4271-4292.
https://doi.org/10.3390/e17064271