Power-law of Aggregate-size Spectra in Natural Systems

Convertino, Matteo; Simini, Filippo; Catani, Filippo; Linkov, Igor; Kiker, Gregory A.

doi:10.4108/trans.cs.1.2.e2

Cited by 7 publications

(31 citation statements)

References 102 publications

(178 reference statements)

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“…The exponents ε and β of the double‐Pareto distribution of the landslide size determine the probability to observe large and small landslides, respectively (equation in section 2.5). Double‐Pareto distributions for landslides are widely reported in literature [ Guzzetti et al , ; Stark and Guzzetti , ; Convertino et al , ], although there is a debate about the origin of such distribution. The best set of exponents of the double‐Pareto distribution that fits the observed distributions is estimated by a Kolmogorov‐Smirnov (KS) test (supporting information).…”

Section: Resultsmentioning

confidence: 99%

“…We propose the landslide size distribution and its scaling exponents as potential indicators of change to inform about the landslide hazard of SES in river basins. Studies in other fields have emphasized the connection of size distributions of natural process variables to external changes [ Kéfi et al , ; Convertino et al , ]. In our case study of rainfall‐triggered landslides, we show how the scaling exponents of the landslide size distribution decrease and increase as a function of climate change wet and dry periods, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…The probability density of landslide size can be universally described [ Stanley , ] by the double‐Pareto distribution introduced by Convertino et al [] in the form:

\begin{matrix} alignleft \\ align-1 p (s) & align-2 = \frac{s^{β - 1} Θ (s) Θ (t - s) + s^{- ε - 1} Θ (m - s) Θ (s - t)}{[\frac{t^{β}}{β} + \frac{m^{- ε} - t^{- ε}}{ε}]} \\ align-1 & align-2 \sim \{\begin{matrix} s^{β - 1} & for s < t \\ s^{- ε - 1} f ((), \frac{s}{m}) & for s > t \end{matrix}, \end{matrix}

where t is the truncation point (hard truncation) for which the transition in the scaling regime of the probability distribution is observed and m is the upper cutoff (Table ). We refer to “hard truncation” when the pdf clearly exhibits two regimes (for s < t and s > t ) in which two scaling exponents can be identified for at least 1 order of magnitude [ Convertino et al , ]. Θ( x )=1 if x >0 and zero otherwise where x is any independent function [ Simini et al , ].…”

Section: Methodsmentioning

confidence: 99%

“…The exceedance probability of the landslide size is given by integration of equation :

P (\geq s) = ({, \begin{matrix} N [\frac{t^{β} - s^{β}}{β} + \frac{t^{- ε} - m^{- ε}}{ε}] & for s < t \\ N \frac{s^{- ε} - m^{- ε}}{ε} & for s > t \end{matrix}) \sim ({, \begin{matrix} C_{0} - s^{β} C_{1} & for s < t \\ s^{- ε} F (\frac{s}{m}) & for s > t \end{matrix}),

where

N = {([], \frac{t^{β}}{β} + \frac{m^{- ε} - t^{- ε}}{ε})}^{- 1}

, C 0 and C 1 are constants, and F is a homogeneity function that depends on a characteristic size

m \sim S \sim L_{∥}^{1 + H}

( L ∥ is the diameter of a landslide along its principal axis of inertia, and H is the Hurst exponent) [ Convertino et al , ], and ε = D f /2 [ Mandelbrot , ; Convertino et al , ]. D f is the fractal dimension of the landslide pattern that is on average the fractal dimension of each landslide because of the scale invariance of landslide patterns [ Convertino et al , ]. The fractal dimension of each landslide is found from the scaling of the landslide perimeter and size as in Convertino et al [].…”

Section: Methodsmentioning

confidence: 99%

“…Figure 3 shows schematically an example of calculation of the landslide size. [27] The probability density of landslide size can be universally described [Stanley, 1999] by the double-Pareto distribution introduced by Convertino et al [2013] in the form:…”

Section: Landslide Size Distributionmentioning

confidence: 99%

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Detecting fingerprints of landslide drivers: A MaxEnt model

2013

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[1] Landslides are important geomorphic events that sculpt river basins by eroding hillslopes and providing sediments to coastal areas. However, landslides are also hazardous events for socio-ecological systems in river basins causing enormous biodiversity, economic, and social impacts. We propose a probabilistic spatially explicit model for the prediction of landslide patterns based on a maximum entropy principle model (MAXENT). The model inputs are the centers of mass of historical landslides and environmental variables at the basin scale. The model has only three parameters requiring calibration: the threshold for the network extraction, the trade-off factor between model complexity and accuracy, and the threshold of landslide susceptibility. The calibration on a subset of observations detects the environmental drivers and their relative importance for landslides. We employ the model in the Arno basin, Italy, selected because of its widespread landslide dynamics and the large availability of landslide observations. The model reproduces the size distribution and location of over 27,500 historical landslides for the Arno basin with an accuracy of 86% obtained from the variable-landslide inference on about 37% of observed landslides. Future landslide patterns are predicted for 17 A1B and A2 rainfall scenarios and for a multimodel ensemble from 2000 to 2100. We show that potential landslide hazard is strongly correlated with variation in the 12 and 48 h rainfall with a return time of 10 years. As the climate gets wetter, the average probability of landslides gets higher which is shown by the landslide size distribution. Hence, the landslide size distribution is a fingerprint of the geomorphic effectiveness of rainfall as a function of climate change. MAXENT is proposed as a parsimonious model for the prediction of landslide patterns with respect to more complex models. The need for very accurately sampled and delineated landslides is lower than for other prediction models. Moreover, the model informs about the drivers of landslides and their relative importance without assumptions on the main triggering factors. This is important to inform monitoring of environmental variables. Our modeling approach can enhance the planning of socio-ecological systems in river basins by improving the accuracy of landslide prediction in space and time.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…The probability density of landslide size can be universally described [ Stanley , ] by the double‐Pareto distribution introduced by Convertino et al [] in the form:

\begin{matrix} alignleft \\ align-1 p (s) & align-2 = \frac{s^{β - 1} Θ (s) Θ (t - s) + s^{- ε - 1} Θ (m - s) Θ (s - t)}{[\frac{t^{β}}{β} + \frac{m^{- ε} - t^{- ε}}{ε}]} \\ align-1 & align-2 \sim \{\begin{matrix} s^{β - 1} & for s < t \\ s^{- ε - 1} f ((), \frac{s}{m}) & for s > t \end{matrix}, \end{matrix}

Section: Methodsmentioning

confidence: 99%

“…The exceedance probability of the landslide size is given by integration of equation :

P (\geq s) = ({, \begin{matrix} N [\frac{t^{β} - s^{β}}{β} + \frac{t^{- ε} - m^{- ε}}{ε}] & for s < t \\ N \frac{s^{- ε} - m^{- ε}}{ε} & for s > t \end{matrix}) \sim ({, \begin{matrix} C_{0} - s^{β} C_{1} & for s < t \\ s^{- ε} F (\frac{s}{m}) & for s > t \end{matrix}),

where

N = {([], \frac{t^{β}}{β} + \frac{m^{- ε} - t^{- ε}}{ε})}^{- 1}

, C 0 and C 1 are constants, and F is a homogeneity function that depends on a characteristic size

m \sim S \sim L_{∥}^{1 + H}

Section: Methodsmentioning

confidence: 99%

Section: Landslide Size Distributionmentioning

confidence: 99%

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Detecting fingerprints of landslide drivers: A MaxEnt model

2013

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Landslide damming hazard susceptibility maps: a new GIS-based procedure for risk management

Stefanelli

Catani

2020

Landslides

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A complete landslide dam hazard management incorporates two assessment phases: the damming probability and the breach hazard. A prompt evaluation of the dam stability is crucial during the emergency to mitigate its consequences, but a reliable risk assessment can be realized only after the event has occurred, when the available time is very short. Therefore, it is necessary to develop tools able to help in mapping the spatial probability of damming over large areas for land-use planning, in order to better constrain consequence analysis and risk scenarios for setting up mitigation measures. In this work, a semi-automated GIS-based mapping methodology, based on a statistical correlation of morphometric parameters described by a morphological index, is proposed to spatially assess the likelihood of a river obstruction by landslide damming through two main mechanisms: the reactivation of existing landslides and the formation of new landslides. The two mapping methods (damming predisposition and damming probability) were used on a test area, the Arno River basin in Italy. The Eastern part of the basin resulted as the most susceptible to damming events in the whole basin. These are the highest mountain ridges in the basin (about 1600 m a.s.l.), characterized by calcareous, arenaceous, and marl lithology. The results are confirmed by the high concentration of the known historical landslide dams in the area according to existing inventories.

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