Using multinomial logistic regression for prediction of soil depth in an area of complex topography in Taiwan

Highlights

• Soil depth was modelled in a regional scale with complex topography.

• Predictive performance of four statistical techniques was compared.

• Multinomial logistic regression proved in soil depth estimation.

• Soil depth conditioned by the topographical and geomorphological characteristics.

Abstract

Increasing land developments, unreasonable utilization of land, earthquakes, typhoons, and torrential rain often cause hillside disasters. Soil depth is a crucial parameter influencing the scale of shallow landslides and sustainable land use in hillside areas. This paper presents a statistical model, integrated with environmental factors, for estimating soil depth in a catchment area with complex topography. The study area selected was upstream of the Houlong River in Taiwan. The model was developed using multinomial logistic regression and environmental factors such as hill slope, hill aspect, elevation, topographical curvature, and the normalized difference vegetation index. The results were then compared with those obtained from previous models applying Ordinary Kriging, Regression Kriging, and topographical wetness index methods. A classification error matrix and the Kappa index were then employed to assess the various models. The results showed that, for the data set used for model establishment, the overall accuracy and Kappa index were 76.6% and 0.65, respectively, whereas for the data set used for verification, they were 70.5% and 0.57, respectively. By contrast, the Ordinary Kriging method yielded an overall accuracy and a Kappa index of 45.7% and 0.15, respectively; the Regression Kriging method yielded results of 46.7% and 0.16, respectively; and the topographical wetness index method yielded results of 30.5% and −0.05, respectively. The proposed model was therefore determined to be superior to the others in terms of soil depth estimation accuracy. The proposed model can predict soil depth on a regional scale and serve as a reliable tool that provides reference data for future research on land use and shallow landslides.

Introduction

Taiwan is a mountainous island, where nearly 70% of the land is occupied by hills and mountains. Because of increasing population size and lack of flat land, development was pushed onto hillsides. However, the unstable geological environment on hillsides, unreasonable utilization of land, earthquakes, typhoons, and torrential rains have frequently jeopardized the lives and properties of hillside residents (Lin et al., 2017).

Soil depth is a crucial factor affecting the occurrence of shallow landslides and hillside disasters. For example, Dymond et al. (1999) found that, when a landslide occurs, the shear stress of soil equals its shear strength; soil shear stress increases with hillside slope; and shear strength decreases as soil depth increases. Therefore, the greater the slope or soil depth is, the greater the soil shear stress on a hillside becomes, making a landslide more likely to occur. Uchida et al. (2009) indicated that a shallow landslide occurs when soil collapses on weathered rocks; thus, the landslide body is often soil or the top layer of weathered rocks. The volume of a landslide body influences the amount of landslide debris produced and thus the safety of residents located downstream of the landslide. An accurate estimation of the volume of a landslide body can help people respond to landslide disasters; moreover, the volume is related to the landslide area and soil depth. However, a survey of soil depth requires both personnel and resources and is a time-consuming process. In addition, soil depth data are relatively scarce. Therefore, previous landslide studies have either ignored the influence of soil depth or employed a certain value to represent soil depth (Bakker et al., 2005; Talebi et al., 2008). Soil depth is also crucial in the classification of land use capability. For example, to maintain long-term land productivity, New Zealand graded land use capability according to erodibility, wetness, soil limitations within a rooting zone, and climate (Lynn et al., 2009). The soil limitation within a rooting zone is affected by soil depth. To control land use and prevent hillside disasters, the Taiwanese government implemented a regulation to limit land use on hillsides, with soil depth being considered a crucial factor in determining land use limitations. To facilitate the management of land use in Taiwan, soil depth was classified into four categories: extremely deep soil (>90 cm), deep soil (50–90 cm), shallow soil (20–50 cm), and extremely shallow soil (<20 cm) (Council of Agriculture, 2017).

Three approaches are commonly used to estimate soil depth: physically based, empirico-statistical, and spatial interpolation methods. The physically based method was first proposed by Gilbert (1909), who considered soil thickness to be related to soil longitudinal formation and horizontal movement, thus creating a balanced state. Subsequently, Ahnert (1970) and Carson and Kirkby (1972) have used exponentially decreasing and bell-shaped curves to represent the relationship between soil formation rate and soil thickness. Later, this method was developed into a soil production function to simulate soil thickness. Soil movement was considered as gravity-controlled movement. Numerous researchers have used the diffusion model of thermodynamics to describe this effect (Dietrich et al., 1995; Heimsath et al., 1997). Particularly, Dietrich et al. (1995) proposed a model that estimates soil depth by integrating the soil production function and soil diffusion model according to the principle of mass conservation. Braun et al. (2001) indicated that the physically based method is suitable for predicting soil depth at landscape units (map units). Moreover, this method is based on the influence of gravity; accordingly, a large volume of field data is required to calibrate model parameters. Preparing data for this method is thus a time-consuming process and requires a high number of personnel. Nevertheless, the physically based method is suitable for estimating the depth of soil formed by a long-term evolutionary process in a large area. By contrast, the empirico-statistical method estimates soil depth according to a specific phenomenon in a region and can be further subdivided into an inferential method and environmental correlation method. In the inferential method, specific indicators are used to estimate average soil depth, and this method can be used in regions with homogeneous environmental conditions. For example, in a large area covered by identical plant species, the relationship between indicators and soil depth can be clearly defined. Treiber and Krusinger (1975) used plant species to estimate soil depth. However, soil depth is usually attributed to different environmental conditions. Hence, the inferential method cannot accurately measure soil depths in an environment with heterogeneous conditions, for example in mountainous areas. In the environmental correlation method, statistical methods are integrated with environmental factors to identify the relationship between these factors and soil depth. Delmonaco et al. (2003) used measured soil depth data as well as slope data obtained from a digital elevation model to establish a relationship between slope and soil depth through a regression model. The regression model was then used to estimate the spatial distribution of soil depth in Tuscany, Italy, where the elevation of hillsides is approximately 2000 m and the average slope is between 30° and 35°. Lee and Ho (2009) also established a relationship between the topographic wetness index and soil depth for mountain areas in northern Taiwan by using a regression model. They estimated the spatial distribution of soil depth and applied this to a model for forecasting shallow landslides. The environmental correlation method has also been employed for regions with heterogeneous environmental conditions. This method enables estimating the soil depth in a region characterized by complex topography by using relevant environmental data (e.g., topographic and vegetation factors). For the spatial interpolation method, the measured soil depths at specific locations are employed to estimate the soil depths of other locations (obtained via an interpolation method) according to their geographical characteristics. One of the most used estimators for interpolating soil depth are Kriging techniques (Knotters et al., 1995; Bourennane et al., 2000; Kuriakose et al., 2009). They employ variances to identify the weighting relationship between the soil depths at unknown locations and measured locations and to estimate the soil depth at unknown locations. Two main types of Kriging technique exist: the Ordinary Kriging method, in which a single variable is used to estimate soil depth, and the Regression Kriging method, in which two or more variables are used for improving the estimating results. These methods produce low estimation errors but ignore the effect of topography on soil. In a region with large topographical variation, if the measured locations are not evenly distributed, some spatial characteristics may be disregarded, resulting in unsatisfactory results.

Soil depth plays a critical role in hillside disasters and land use management. Accordingly, the objective of this study was to develop a soil depth estimation model. Owing to the complex topographical variation in Taiwan, the environmental correlation method was employed to estimate soil depth. This study developed the model, determined factors related to soil development, and investigated the distribution of soil depth in the study area. For comparison, Ordinary Kriging, Regression Kriging, and topographical wetness index methods were also used to estimate soil depth, and the estimations were then used to assess the accuracy of the proposed model. The proposed model is expected to serve as a reference for hillside land use management or research on potential hillside disasters.