Assessment of trampling impact in Icelandic natural areas in experimental plots with focus on image analysis of digital photographs

Increasing tourism in the spectacular but sensitive ecosystems in Iceland arises concern to the country’s authorities how to best manage tourism in these natural areas within a level of acceptable change. Research is thus required regarding what affect tourism has on different environments. Deterioration of natural areas in Iceland from trampling by numerous hikers are causing visible vegetation loss, widening and deepening of existing hiking trails with subsequent soil erosion. In this study, the primary goal was to assess impact to three typical Icelandic vegetation types (grassland, mossheath and moss) due to recreational short-duration trampling pressure. Measurements in experimental plots of soil compaction, soil moisture, soil surface depth, and vegetation cover were analysed for different hiking pressures. The study areas include the two most popular areas of nature-based tourism in Iceland; Þingvellir [ˈθiŋkˌvɛtlɪr̥] National Park and Fjallabak Nature Reserve. One of the main issues in field measurement techniques is how to achieve a cost- and time effective method to estimate vegetation cover with adequate accuracy. The second goal of this study was to assess the performance of digital photography and subsequent image analysis as a tool for estimating vegetation cover, a method not previously used in the field of recreational trampling research. Three different methods are evaluated; supervised classification of the images, segmentation of the images using the ExGR (Excess Green minus Excess Red) index and extraction of greenness information from the images through application of the Green Chromatic Coordinate (GCC). The results, together with previous research show that image analysis of digital photography is a valuable tool for detecting changes in vegetation. All three methods applied show ability to assess vegetation cover, the supervised classification method being the most accurate method for quantitative measurements. The Icelandic vegetation types consist greatly of moss species of various colors not enhanced when greenness indices are applied to the RGB images. Nevertheless, the greenness index methods resulted in the same conclusion as the supervised classification method as regards the relationship between vegetation cover and trampling pressure, and in the evaluation of the resistance of each vegetation type. All vegetation types show being significantly altered with added trampling pressure in terms of change of the physical properties of soil and of vegetation cover. The mossheath vegetation type, and especially the type in the highland (Fjallabak Nature Reserve) is verified as being the least resistant to trampling pressure. Relationships of soil compaction, surface depth and vegetation cover with trampling were curvilinear, suggesting higher rates of damage at initial stages of trampling.Increasing tourism in the spectacular but sensitive ecosystems in Iceland arises concern to the country’s authorities how to best manage tourism in these natural areas within a level of acceptable change. Research is thus required regarding what affect tourism has on different environments. Deterioration of natural areas in Iceland from trampling by numerous hikers are causing visible vegetation loss, widening and deepening of existing hiking trails with subsequent soil erosion. In this study, the primary goal was to assess impact to three typical Icelandic vegetation types (grassland, mossheath and moss) due to recreational trampling pressure. Measurements in experimental plots of soil compaction, soil moisture, soil surface depth, and vegetation cover were analysed for different hiking pressures. The study areas include the two most popular areas of nature-based tourism in Iceland; Þingvellir [ˈθiŋkˌvɛtlɪr̥] National Park and Fjallabak Nature Reserve. The second goal of this study was to assess the performance of digital photography and subsequent image analysis as a tool for estimating vegetation cover, a more accurate, cost- and time effective method not previously used in the field of recreational trampling research. Three different methods are evaluated; the more traditional way of classifying land cover types depending on their spectral reflectance (supervised classification), and two methods where greenness formulas are applied on the spectral reflectance values of the pixels to enhance the greenness information within the digital images (ExGR and GCC index). The results, together with previous research, show that image analysis of digital photography is a valuable tool for detecting changes in vegetation. All three methods applied show ability to assess vegetation cover, the supervised classification method being the most accurate method for quantitative measurements. The Icelandic vegetation types consist greatly of moss species of various colors not enhanced when greenness indices are applied to the digital images. Nevertheless, the greenness index methods resulted in the same conclusion as the supervised classification method as regards the relationship between vegetation cover and trampling pressure, and in the evaluation of the resistance of each vegetation type. All vegetation types show being significantly altered with added trampling pressure in terms of change of the physical properties of soil and of vegetation cover. The mossheath vegetation type, and especially the type in the highland (Fjallabak Nature Reserve) is verified as being the least resistant to trampling pressure. Relationships of soil compaction, surface depth and vegetation cover with trampling were curvilinear, suggesting higher rates of damage at initial stages of trampling

Lower bound for the maximal number of facets of a 0/1 polytope

We show that there exist 0/1 polytopes in R^n with as many as (cn / (log n)^2)^(n/2) facets (or more), where c>0 is an absolute constant.Comment: 19 page

Local structure of self-affine sets

The structure of a self-similar set with open set condition does not change under magnification. For self-affine sets the situation is completely different. We consider planar self-affine Cantor sets E of the type studied by Bedford, McMullen, Gatzouras and Lalley, for which the projection onto the horizontal axis is an interval. We show that within small square neighborhoods of almost each point x in E, with respect to many product measures on address space, E is well approximated by product sets of an interval and a Cantor set. Even though E is totally disconnected, the limit sets have the product structure with interval fibres, reminiscent to the view of attractors of chaotic differentiable dynamical systems.Comment: 10 pages, 2 figure

Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet

In this note, we show that on certain Gatzouras-Lalley carpet, there exist more than one ergodic measures with full Hausdorff dimension. This gives a negative answer to a conjecture of Gatzouras and Peres

Dimensions and singular traces for spectral triples, with applications to fractals

Given a spectral triple (A,D,H), the functionals on A of the form a -> tau_omega(a|D|^(-t)) are studied, where tau_omega is a singular trace, and omega is a generalised limit. When tau_omega is the Dixmier trace, the unique exponent d giving rise possibly to a non-trivial functional is called Hausdorff dimension, and the corresponding functional the (d-dimensional) Hausdorff functional. It is shown that the Hausdorff dimension d coincides with the abscissa of convergence of the zeta function of |D|^(-1), and that the set of t's for which there exists a singular trace tau_omega giving rise to a non-trivial functional is an interval containing d. Moreover, the endpoints of such traceability interval have a dimensional interpretation. The corresponding functionals are called Hausdorff-Besicovitch functionals. These definitions are tested on fractals in R, by computing the mentioned quantities and showing in many cases their correspondence with classical objects. In particular, for self-similar fractals the traceability interval consists only of the Hausdorff dimension, and the corresponding Hausdorff-Besicovitch functional gives rise to the Hausdorff measure. More generally, for any limit fractal, the described functionals do not depend on the generalized limit omega.Comment: latex, 36 pages, no figures, to appear on Journ. Funct. Analysi

Curvature-direction measures of self-similar sets

We obtain fractal Lipschitz-Killing curvature-direction measures for a large class of self-similar sets F in R^d. Such measures jointly describe the distribution of normal vectors and localize curvature by analogues of the higher order mean curvatures of differentiable submanifolds. They decouple as independent products of the unit Hausdorff measure on F and a self-similar fibre measure on the sphere, which can be computed by an integral formula. The corresponding local density approach uses an ergodic dynamical system formed by extending the code space shift by a subgroup of the orthogonal group. We then give a remarkably simple proof for the resulting measure version under minimal assumptions.Comment: 17 pages, 2 figures. Update for author's name chang

The Hausdorff and dynamical dimensions of self-affine sponges : a dimension gap result

We construct a self-affine sponge in R 3 whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem that previous techniques could only solve in two dimensions. The Hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge, implying that sponges with a dimension gap represent a nonempty open subset of the parameter space