Comparing landslide size probability distribution at the landscape scale (Loess Plateau and the Qinba Mountains, Central

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ORIGINAL PAPER

Comparing landslide size probability distribution at the landscape scale (Loess Plateau and the Qinba Mountains, Central China) using double Pareto and inverse gamma Haijun Qiu 1,2,3

&

Sheng Hu 1,2 & Dongdong Yang 1,2 & Yi He 1,2 & Yanqian Pei 1,2 & Ulrich Kamp 3

Received: 20 August 2018 / Accepted: 29 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract Landsliding is a prominent geomorphological process in both the Loess Plateau and the Qinba Mountains in Central China. The size distribution of landslides plays an important role in quantifying their occurrence and magnitude, estimating erosion and sediment yields, and determining hazards. We generated landslide inventories for six study sites within the two study regions based on results from field surveying and remote sensing analyses. Landside size distribution differs considerably in both regions and can be described by the double Pareto and inverse gamma distributions. The power law decays faster in the Loess Plateau than in the Qinba Mountains; the locations of the rollover occur at larger landslide size in the Loess Plateau. Moreover, α, an exponent of power law scaling related to slope in the double Pareto function, is strongly related to ρ + 1, a control of power law decay in the inverse gamma. This study provides an insight into the landslide size probability distribution in different landscape types. Keywords Landslide size . Probability distribution . Rollover effect . Loess Plateau . Qinba Mountains

Introduction Landslides, as a complex natural phenomenon, represent a serious natural hazard (Malamud et al. 2004; Guzzetti et al. 2012). However, their impact is greater in developing countries in consequence of higher economic, social, and cultural vulnerabilities to natural disasters (Alcantara-Ayala 2002). Across the developing world, factors such as rapid population growth and urban sprawl resulted in a significant increase in landslide occurrence over the past two decades (Broothaerts et al. 2012; Greco et al. 2013; Conforti et al. 2014). The Loess Plateau and the Qinba Mountains in central China are highly vulnerable to hazards resulting from widespread landsliding, and in both regions, resources to recover from landslide events

* Haijun Qiu [email protected] 1

Shaanxi Key Laboratory of Earth Surface System and Environmental Carrying Capacity, Northwest University, Xi’an 710127, China

2

Institute of Earth Surface System and Hazards, Northwest University, Xi’an 710127, China

3

Department of Natural Sciences, University of Michigan-Dearborn, Dearborn, MI 48128, USA

are limited, which calls for the development of landslide hazard mitigation strategies (Qiu et al. 2018, 2019a). Both landslide size and size distribution play important roles in quantifying their occurrence and magnitude, estimating erosion and sediment yields, and determining hazards (Malamud and Turcotte 1999; Guzzetti et al. 2002; Van Den Eeckhaut et al. 2007; Hungr et al. 2008; Frattini and Crosta 2013). Based on results from