Fractal properties of isolines at varying altitude revealing different dominant geological processes on Earth

Baldassarri, Andrea; Montuori, M.; Prieto-Ballesteros, O.; Manrubia, Susanna C.

doi:10.1029/2007je003066

Cited by 14 publications

(8 citation statements)

References 33 publications

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“…This indicates not only a correlation in time (seasons) but also a dependence of the parameters describing, for example, the average vegetation versus the minimum vegetation. Roughness and altitude are robustly related because rougher terrains are typically located at higher altitude [23]. LD displays high positive correlations with most variables measured, with the exception of minimum precipitation and altitude.…”

Section: (A) Correlations Between Variables and Global Linguistic Diversitymentioning

confidence: 90%

River density and landscape roughness are universal determinants of linguistic diversity

Axelsen

Manrubia²

2014

Proc. R. Soc. B.

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Global linguistic diversity (LD) displays highly heterogeneous distribution patterns. Though the origin of the latter is not yet fully understood, remarkable parallelisms with biodiversity distribution suggest that environmental variables should play an essential role in their emergence. In an effort to construct a broad framework to explain world LD and to systematize the available data, we have investigated the significance of 14 variables: landscape roughness, altitude, river density, distance to lakes, seasonal maximum, average and minimum temperature, precipitation and vegetation, and population density. Landscape roughness and river density are the only two variables that universally affect LD. Overall, the considered set accounts for up to 80% of African LD, a figure that decreases for the joint Asia, Australia and the Pacific (69%), Europe (56%) and the Americas (53%). Differences among those regions can be traced down to a few variables that permit an interpretation of their current states of LD. Our processed datasets can be applied to the analysis of correlations in other similar heterogeneous patterns with a broad spatial distribution, the clearest example being biological diversity. The statistical method we have used can be understood as a tool for cross-comparison among geographical regions, including the prediction of spatial diversity in alternative scenarios or in changing environments.

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Section: (A) Correlations Between Variables and Global Linguistic Diversitymentioning

confidence: 90%

River density and landscape roughness are universal determinants of linguistic diversity

Axelsen

Manrubia²

2014

Proc. R. Soc. B.

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“…Jf, 64.60.ah, Discovering the connection between geometrical features of terrestrial surface on the Earth and its geological internal processes has long been a basic challenge area in the Earth sciences [1,2], and attracted the attention of physicists and mathematicians as well [3]. Various theoretical models have emerged to identify the underlying constructive rules responsible for the appearance of self-similarity, scale and conformal invariance in the fractal geometry of the local geomorphic patterns [4][5][6][7][8][9]. In comparison with different models proposed to describe the statistical properties of regional features [10][11][12], the global topography has received less attention and thus remained controversial.…”

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confidence: 99%

Percolation Description of the Global Topography of Earth and the Moon

Saberi

2013

Phys. Rev. Lett.

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Remarkable global correlations exist between geometrical features of terrestrial surfaces on Earth, current mean sea level, and its geological internal processes whose origins have remained an essential goal in the earth sciences. Theoretical modeling of the ubiquitous self-similar fractal patterns observed on Earth and their underlying rules is indeed of great importance. Here I present a percolation description of the global topography of Earth in which the present mean sea level is automatically singled out as a critical level in the model. This finding elucidates the origins of the appearance of scale invariant patterns on Earth. The criticality is shown to be accompanied by a continental aggregation, unraveling an important correlation between the water and long-range topographic evolutions. To have a comparison point in hand, I apply such an analysis to the lunar topography which reveals various characteristic features of the Moon.

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“…The exponent D f , is called the coast fractal dimension. It is often around 1.3, although it may attain higher values for fjorded coastlines (Baldassarri et al, 2008).…”

Section: Scale Invariancementioning

confidence: 99%

Power law statistics of cliff failures, scaling and percolation

Baldassarri

Sapoval

2015

Earth Surf Processes Landf

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Large cliff failures have often been characterized by their size in terms of the horizontal eroded area at the cliff top, and the maximum local retreat of the coastline. Field studies suggest that the frequencies of these two quantities decrease as power laws of their respective magnitudes, defining two different decay exponents. Moreover, the horizontal area increases as a power law of the maximum local retreat, identifying a third exponent. This observation indicates that the geometry of cliff failures are similar for different magnitudes. It is shown that, under a 'scaling hypothesis', the exponents satisfy a precise mathematical relation that relates the exponent of the distributions of magnitudes of events and their geometry -a relation that could be useful to validate the analysis of field catalogs. In order to understand the observed scenario, a numerical model of rocky coast erosion is developed. Despite its minimal character, it reproduces the observed cliff failure statistics. Strikingly, the model precisely reproduces the geometric similarity of cliff failures observed in the field. These results suggest that the theory of percolation, which underlies the erosion model, can possibly be used as a guide to decipher the physics of rocky coast erosion and could provide precise predictions of the statistics of cliff collapses.

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Fractal properties of isolines at varying altitude revealing different dominant geological processes on Earth

Cited by 14 publications

References 33 publications

River density and landscape roughness are universal determinants of linguistic diversity

River density and landscape roughness are universal determinants of linguistic diversity

Percolation Description of the Global Topography of Earth and the Moon

Power law statistics of cliff failures, scaling and percolation

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