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A GIS-based statistical model for rapid landslide susceptibility mapping in the Beichuan-Pingwu area, Sichuan, China

The 2008 Wenchuan earthquake, with a magnitude of Mw 8.0, induced numerous landslides. Remote sensing planes were sent out to take high resolution aerial photographs, from which the geologic hazards could be instantly interpreted. However, aerial images covering all of the study area could not be obtained in a short time because of the limitations of the planes and the influence of weather conditions. This studyestablishes a statistical model based on the landslide interpretation results of one photographic strip inside the Beichuan-Pingwu area. It has strong applicability and can be applied to other places without such data. Finally, we produced a landslide susceptibility map, which providesscientific support for the instant evaluation of disaster information and post-disaster reconstruction.


Introduction
The Wenchuan earthquake, measured at Ms 8.0 according to the China Earthquake Administration, occurred at 14:28 on12 May 2008 in Sichuan Province of southwestern China. It brought overwhelming destruction to eight provinces and cities. Landslides triggered by the earthquake, which disrupted transportation, power, and communications,were distributed along the fault rupture zone and river channels.Remote sensing planeswere sent out to take high resolution aerial photographs, from whichthe geologic hazards could be instantly interpreted. However, aerial images covering all of the study areacould not be obtained in a short time because of the limitations of the planes and the influence of weather conditions. In this study, we established a statistical model based on the landslide interpretation results of one airborne photographic strip inside the Beichuan-Pingwu area. It has strong applicability and can be applied to other places without such data. Finally, we produced a landslide susceptibility map, which providesscientific support for the instantevaluationof disaster information and post-disaster reconstruction.

The study area
Our study area, with a total area of 4,630 km 2 , is situated 167 kmnortheast of the earthquake's epicenter ( Figure 1). The area includes a part ofBeichuan County, Jiangyou County, and Pingwu County in Sichuan Province. The study area is situated in the transitional mountainous beltbetween the Sichuan Basin and the Western Sichuan Plateau, characterized by rugged mountains with elevations between 300 mand 4,700 m as well as deeply incised valleys. Theepicenter of this strong earthquake was just inthe medium to high mountains west of the SichuanBasin, where the geological environment

Methods
A variety of approaches have been used for landslide susceptibility mapping, and they can be classified into qualitative and quantitative methods. Most qualitative methods tend to be subjective since they depend on expert opinions and portray hazard levels in descriptive terms. Quantitative methods arebased on the numerical expression of the relationshipbetween instability factors and landslides, which can bedivided into deterministic and statistical [2] . Deterministic methods depend on engineering principles of slope instability, expressed in the factor of safety, and are thereforemostly used for individual slope limited to a local site [3,4] . Statistical methods based on the assumption that the past occurrence of landslides in a specific site is indicative of the potential for future landslides to occur in sites with similar characteristicshave been widely used in regional scale landslide susceptibility mapping [5,6,7] . The most important step in forming a statistical model isto establish relationships between variables based on statistics of mapped landslide inventory data.These variables refer to factors leading to landslides and include continuous data (such as altitude, slope angle, and slope aspect)and discrete data (such as lithology).Most previous statistical models transformed continuous factor data into categorized classes [8] . Such conversions inevitably result in loss of information. In this study,a GISbased statistical model was proposed based on single factor landslide susceptibility curve fitting and multivariate logistic regression. The data processing is shown below.

Choosing evaluation factors
Landslide occurrence depends on complex interactions among a large number offactors. As shown in Figure 3, six factors influencing landslide occurrence, including altitude, slope, aspect, distance from fault, lithology, and normalized difference vegetation index (NDVI), were extracted in this study from digital terrain models (DTM), remote sensing images, and geologic data.

Calculating the susceptibility of each single factor
For continuous evaluation factors such as altitude, slope, aspect, distance from fault, and NDVI, a curve fitting method to fit the landslide ratio and each single factor was used. The curve fitting function was chosen depending on how the factor influences the landslide. For instance, a quadratic or cubicfunction was selected to fit the slope, aspect, and altitude, whereas a logarithmic or linear function was used to fit the distance from fault and NDVI. Some factors were abandoned once the precision of curve fitting was low, for example, the altitude in this study. For a discrete evaluation factor of lithology, the landslide ratio of each lithology was calculated directly. Take the continuous factor slope angle as anexample.First, slope angle wasdivided into more than 32classes between 0 and 90 degrees as its value range. Second, the landslide frequency of each class was calculated. Third, several kinds of profiles such as linear,logarithmic,quadratic, and cubic curveswere used to fit the landslide frequency.The curve fitting result is shown in Table 1. The best curve fitting equation was chosen to calculate the landslide susceptibilityagainstthe slope angle. In this study, the cubic equation was chosenbecauseits R-squared reached 0.76, which was much more than the R-squared of the quadratic equation. So the function below was used to calculate the landslide susceptibility against slope angle. The result is shown as Figure 4.

Logistic regression of multiple factors
The principle of logistic regression (LR) rests onthe analysis of a problem in which a result measuredwith dichotomous variables such as 0 and 1 or trueand false is determined from one or more independentfactors [9] . In this study, LR was used to find the best-fitting model to describe the relationship between the presence or absence of landslides (dependent variable) and a set of independent parameters as susceptibility of each single factor (quantified in Step 2). The region of the modeling area was divided into 20*20-m pixels and there were 5,488 pixels considered to be alandslide occurrence, while5,488 pixels were selected without landslides to be included in LR together with the pixels of landslide occurrence. In order to implement this regression method, SPSS software was employed to calculate the correlation between the landslide and each factor. The LR function was built as follows. 1 Thecreated landslide susceptibility map was classified into four classes based on the statistic of susceptibility, including very low (0.00-0.17), low (0.18-0.37), high (0.38-0.57), and very high(0.58-1.00). The majority of landslides occurred withinareas designated as very high susceptibility.The resultant landslide susceptibility map, togetherwith the landslide inventory, is shown in Figure  5.However, wealso observed some landslides in high-to low-susceptibilityareas.  To evaluate the accuracy of the result quantitatively, acumulative proportion diagram was used ( Figure  6). It wasfound that when the most susceptible areas cover 10.48% of the total modeling area thecumulative percent of landslide occurrence is 22.60%. The area undercurve (AUC) was calculated to quantitatively represent the predictionaccuracy of the proposed model in the area. The areaunder curve (0.7073) showed good predictive capacity.

Discussion and conclusion
The first results of our model were the single factor fitting coefficients of each factor (Table 1), which were useful for influencing factor selection.In this study, the altitude factor was abandoned because of its poor single factor curve fitting accuracy calculated in Step 3.2. The slope angle, aspect, lithology, distance from fault, and NDVI were chosen as influentialfactors.The second results were the logistic regression model statistics and coefficients (Table 2), which were useful inassessing the accuracy of the regression function and therole of influential factorsinthe presence or absence oflandslides. In this study, the slopeangle factor wasfound to have the strongest relationship with landslides followed by distance to fault and NDVI. Landslides will easily and frequently occur in the quake-hit areain the following years. Large landslide events mayblock river channels and roads. The methods described in this papercould be used for rapid landslide susceptibility mapping.The predicted susceptibilities generated from themodel within the GIS were used to produce a map ofrelative landslide susceptibility for a broad area.