EARTH SURFACE PROCESSES AND LANDFORMS Earth Surf. Process. Landforms 35, 1138–1156 (2010) Copyright © 2010 John Wiley & Sons, Ltd. Published online 15 June 2010 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/esp.1998 Temporal correlations and clustering of landslides Annette Witt, 1,2 Bruce D. Malamud, 2 Mauro Rossi, 3 Fausto Guzzetti 3 and Silvia Peruccacci 3 1 Department of Nonlinear Dynamics, Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany 2 Department of Geography, King’s College London, London, UK 3 Istituto di Ricerca per la Protezione Idrogeologica, Consiglio Nazionale delle Ricerche, Perugia, Italy Received 15 March 2009; Revised 4 January 2010; Accepted 14 January 2010 *Correspondence to: Bruce D. Malamud, Department of Geography, King’s College London, Strand, London WC2R 2LS, UK. E-mail: bruce.malamud@kcl.ac.uk ABSTRACT: 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 (D L ) and in an ‘event’ (S event ) of consecutive days with landsliding. The non-zero values in both time series D L and S event 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 D L and S event time series with 1000 shuffled (uncorrelated) versions. We conclude that the landslide intensity series D L has strong temporal correlations and S event has likely temporal correlations. To examine temporal clustering in D L and S event , 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 [D L ] and γ < 1·0 [S event ]; thus D L and S event each have temporal correlations, but S event 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 D L linear correlations in τ, but for S event inconclusive results. However, using Kendall’s rank correlation analysis we find for both D L and S event the series of τ are strongly correlated. Finally, we apply Fano Factor analysis, finding for both D L and S event 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 occur- rence, 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. KEYWORDS: landslides; hazard; temporal clustering; correlations; persistence Introduction In many parts of the world, landslides are frequent and cause significant impact on the environment and society (Brabb and Harrod, 1989). Most commonly, landslides occur as the result of a trigger (e.g. an earthquake, heavy rainfall, snow melt event), with a triggered landslide event including one to many tens of thousands of landslides (Malamud et al., 2004). The number of landslides occurring in the brief span of time (e.g. minutes to weeks) is one intensity measure of the triggered landslide event. For hazard assessment and landslide models, it is important to understand whether landslide event intensities in a given geo- graphic area have any correlations with themselves, or if the landslide occurrences are clustered in time (Guzzetti et al., 2003, 2005a). Both of these, landslide temporal correlations and clustering, will be explored in this paper. In an uncorrelated time series (e.g. a white noise), values are independent of one another, i.e. it is equally likely at each time step to have values above or below the median value. If landslide intensities are uncorrelated, this means that when a large landslide intensity value (i.e. an event with lots of land- slides) occurs above the median landslide intensity, it is equally probable to have following this a landslide intensity value that is above or below the median, i.e. large (more landslides) or small (zero or few landslides). In a time series that exhibits positive correlations, adjacent values will have landslide intensities that are on average closer to each other (in intensity) than for an uncorrelated time series; large values tend to follow large ones, and small follow small. Temporal correlations are also referred to as persistence or memory (see Malamud and Turcotte, 1999, and references cited therein). An example of five time series, with varying degrees of correlation (and no correlation) is given in Figures 1A–1E. An alternative to examining the temporal correlations of landslide event intensities, is to examine if the landslide occurrences over a given threshold cluster in time. An example of cluster- ing, in unequally spaced wind speed strong storm/hurricane data over a given threshold, is given in Figure 2.