Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping

Mark, David; Aronson, Peter B.

doi:10.1007/bf01033029

Cited by 315 publications

(215 citation statements)

References 17 publications

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“…The fine root samples do not show any significant differences in the box counting dimension between the species, whereas the coarse root systems do. A discrepancy in fractal dimension between coarse and fine root scale seems to occur at least for Grewia flava and Strychnos cocculoides, possibly due to a multifractal behaviour of the root systems, which is not unusual in natural phenomena [27,34,35].…”

Section: Discussionmentioning

confidence: 99%

Structure and fractal dimensions of root systems of four co-occurring fruit tree species from Botswana

et al. 2000

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-Coarse root systems of four different fruit tree species from southern Africa were completely excavated and semi-automatically digitized. Spatial distributions of root length were determined from the digitally-reconstructed branching systems. Furthermore, the fractal characteristic of the coarse root systems was shown by determining the box-counting dimensions. These quantitative methods revealed architectural differences between the species, probably due to different ecophysiological strategies. For fine root samples, which were taken before digging out the whole systems, fractal analysis of the planar projections showed no significant inter-species differences. Methodologically, the study underlines the usefulness of digital 3-D reconstruction in root research. root / digital reconstruction / fractal / architectural analysis / coarse root Résumé -Structures et dimensions fractales des systèmes racinaires provenant de quatre espèces d'arbres fruitiers de Botswana. Des systèmes de grosses racines, provenant de quatre espèces différentes d'arbres fruitiers d'Afrique du Sud, ont été complètement déterrés et digitalisés semi-automatiquement. Les distributions spatiales des longueurs de racines ont été calculées à partir des maquettes informatiques reconstituées. En outre, le caractère fractal des systèmes de grosses racines a été prouvé par une déter-mination de dimensions utilisant la méthode du comptage de boites. Ces méthodes quantitatives révèlent des différences architecturales entre les espèces, résultant probablement de différentes stratégies écophysiologiques. Pour les échantillons de racines fines, obtenus avant l'excavation des systèmes complets, l'analyse fractale des projections planes n'a pas montré de différences significatives entre les espèces. Concernant la méthode, l'étude fait apparaître l'apport de la reconstruction digitale 3-D dans le domaine de la recherche sur les appareils racinaires. racine / reconstruction digitale / fractal / analyse architectural / racine gros

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Section: Discussionmentioning

confidence: 99%

Structure and fractal dimensions of root systems of four co-occurring fruit tree species from Botswana

et al. 2000

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“…[9] Because of typical gaps in the data delivered by the terrestrial laser scanner, the variogram method was used to estimate fractal parameters, which can be applied for irregular data [e.g., Mark and Aronson, 1984;Sun et al, 2006]. The surface investigated must fulfill the conditions of a fractal Brownian surface [Xu et al, 1993].…”

Section: Estimating Fractal Parametersmentioning

confidence: 99%

Persistence in intra‐annual snow depth distribution: 2. Fractal analysis of snow depth development

Schirmer¹,

Lehning²

2011

Water Resources Research

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[1] We present an analysis of high resolution laser scanning data of snow depths of three different slopes in the Wannengrat catchment (introduced in part 1) using omnidirectional and directional variograms for three specific terrain features; cross-loaded slopes, lee slopes, and windward slopes. A break in scaling behavior was observed in all subareas, which can be seen as the roughness scale of bare earth terrain which is modified by the snow cover. In the wind-protected lee slope a different scaling behavior was observed, compared to the two wind-exposed areas. The wind-exposed areas have a smaller ordinal intercept , a smaller short range fractal dimension D, and a larger scale break distance L than the wind-protected lee slope. Snow depth structure inherits characteristics of dominant NW storms, which results, e.g., in a trend toward larger break distances in the course of the accumulation season. This can be interpreted as a result of surface smoothing at increasing scales. Similar scaling characteristics were obtained for two different years at the end of the accumulation season. Since snow depth structure is altered strongly by NW storms, this inter-annual consistency may strongly depend on their frequency in an accumulation period. With the analysis of directional variograms anisotropies of fractal parameters were detected, which were related to dominant wind directions.Citation: Schirmer, M., and M. Lehning (2011), Persistence in intra-annual snow depth distribution: 2. Fractal analysis of snow depth development, Water Resour. Res., 47, W09517,

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“…Klinkenberg (1992) suggested that a phenomenon fits over scales and that its features are nested in discrete scale intervals, leading to a strong correlation between features and phenomena (Mark and Aronson, 1984). In human vision, the neural network is able to distinguish specific features in relation to a corresponding scale (Marr, 1982), as well as to carry out a multiresolution analysis.…”

Section: Introductionmentioning

confidence: 99%

Multiscale analysis of geomorphological and geological features in high resolution digital elevation models using the wavelet transform

Kalbermatten¹,

Ville²,

Turberg³

et al. 2012

Geomorphology

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At the end of the 1990s the emergence of high resolution (1 m) digital elevation models (DEMs) settled the context of high precision geomorphological analysis. These new elevation models permitted to reveal structures that remained heretofore undetectable. Earth scientists henceforth benefit from a source of data with a textural detail that was never attained before. Despite its richness, this information must be treated efficiently to extract features helping geomorphologists to analyze the processes occurring at the surface. Such processes are complex, localized and naturally multiscale. Recently, space-frequential descriptors as wavelets have been proposed successfully for the analysis of DEMs. The wavelet transform is widely used in image processing since it allows us to decompose a signal into a weighted sum of atoms with joint space-frequency localization. Such a decomposition facilitates a coherent navigation from scale to scale, but also permits to detect heretofore undiscerned phenomena at different scales. This is appealing in geomorphology, where structural components, related to a given phenomenon, are well determined in these sub-spaces specific to the scale continuum. In this paper, we propose a filtering procedure of the wavelet decomposition as an approach for the analysis of geomorphological multiscale structures. This filtering procedure enhances the high pass information contained at each scale. The proposed bottom-up approach is applied here to a case study to detect geomorphological structural elements in a valley of the Swiss Jura. It demonstrates that the proposed filtering procedure is an efficient tool for geomorphological multiscale generalization.

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Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping

Cited by 315 publications

References 17 publications

Structure and fractal dimensions of root systems of four co-occurring fruit tree species from Botswana

Structure and fractal dimensions of root systems of four co-occurring fruit tree species from Botswana

Persistence in intra‐annual snow depth distribution: 2. Fractal analysis of snow depth development

Multiscale analysis of geomorphological and geological features in high resolution digital elevation models using the wavelet transform

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