Validating the operational bias and hypothesis of universal exponent in landslide frequency-area distribution

PLoS One. 2014 May 22;9(5):e98125. doi: 10.1371/journal.pone.0098125. eCollection 2014.

Abstract

The exponent decay in landslide frequency-area distribution is widely used for assessing the consequences of landslides and with some studies arguing that the slope of the exponent decay is universal and independent of mechanisms and environmental settings. However, the documented exponent slopes are diverse and hence data processing is hypothesized for this inconsistency. An elaborated statistical experiment and two actual landslide inventories were used here to demonstrate the influences of the data processing on the determination of the exponent. Seven categories with different landslide numbers were generated from the predefined inverse-gamma distribution and then analyzed by three data processing procedures (logarithmic binning, LB, normalized logarithmic binning, NLB and cumulative distribution function, CDF). Five different bin widths were also considered while applying LB and NLB. Following that, the maximum likelihood estimation was used to estimate the exponent slopes. The results showed that the exponents estimated by CDF were unbiased while LB and NLB performed poorly. Two binning-based methods led to considerable biases that increased with the increase of landslide number and bin width. The standard deviations of the estimated exponents were dependent not just on the landslide number but also on binning method and bin width. Both extremely few and plentiful landslide numbers reduced the confidence of the estimated exponents, which could be attributed to limited landslide numbers and considerable operational bias, respectively. The diverse documented exponents in literature should therefore be adjusted accordingly. Our study strongly suggests that the considerable bias due to data processing and the data quality should be constrained in order to advance the understanding of landslide processes.

Publication types

  • Research Support, Non-U.S. Gov't
  • Validation Study

MeSH terms

  • Landslides*
  • Models, Theoretical*

Grants and funding

This study was sponsored by NSC Taiwan grants (NSC 102-2116-M-002-019, 102-2923-M-002-001-MY3) and National Taiwan University (10R70604-2). The websites of NSC and NTU are http://www.most.gov.tw/ and www.ntu.edu.tw. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.