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Temporal correlations and clustering of landslides


Witt,  Annette
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Witt, A., Malamud, B. D., Rossi, M., Guzzetti, F., & Peruccacci, S. (2010). Temporal correlations and clustering of landslides. Earth Surface Processes and Landforms, 35, 1138-1156. doi:10.1002/esp.1998.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-1249-8
This paper examines temporal correlations and temporal clustering of a proxy historical landslide time series, 2255 reported landslides 1951–2002, for an area in the Emilia-Romagna Region, Italy. Landslide intensity is measured by the number of reported landslides in a day (DL) and in an ‘event’ (Sevent) of consecutive days with landsliding. The non-zero values in both time series DL and Sevent are unequally spaced in time, and have heavy-tailed frequency-size distributions. To examine temporal correlations, we use power-spectral analysis (Lomb periodogram) and surrogate data analysis, confronting our original DL and Sevent time series with 1000 shuffled (uncorrelated) versions. We conclude that the landslide intensity series DL has strong temporal correlations and Sevent has likely temporal correlations. To examine temporal clustering in DL and Sevent, we consider extremes over different landslide intensity thresholds. We first examine the statistical distribution of interextreme occurrence times, τ, and find Weibull distributions with parameter γ << 1·0 [DL] and γ < 1·0 [Sevent]; thus DL and Sevent each have temporal correlations, but Sevent to a lesser degree. We next examine correlations between successive interextreme occurrence times, τ. Using autocorrelation analysis applied to τ, combined with surrogate data analysis, we find for DL linear correlations in τ, but for Sevent inconclusive results. However, using Kendall's rank correlation analysis we find for both DL and Sevent the series of τ are strongly correlated. Finally, we apply Fano Factor analysis, finding for both DL and Sevent the timings of extremes over a given threshold exhibit a fractal structure and are clustered in time. In this paper, we provide a framework for examining time series where the non-zero values are strongly unequally spaced and heavy-tailed, particularly important in the Earth Sciences due to their common occurrence, and find that landslide intensity time series exhibit temporal correlations and clustering. Many landslide models currently are designed under the assumption that landslides are uncorrelated in time, which we show is false. Copyright © 2010 John Wiley & Sons, Ltd.