Where is Helvellyn? Fuzziness of multi‐scale landscape morphometry

Abstract

The landscape in which people live is made up of many features, which are named and have importance for cultural reasons. Prominent among these are the naming of upland features such as mountains, but mountains are an enigmatic phenomenon which do not bear precise and repeatable definition. They have a vague spatial extent, and recent research has modelled such classes as spatial fuzzy sets. We take a specifically multiresolution approach to the definition of the fuzzy set membership of morphometric classes of landscape. We explore this idea with respect to the identification of culturally recognized landscape features of the English Lake District. Discussion focuses on peaks and passes, and the results show that the landscape elements identified in the analysis correspond to well-known landmarks included in a place name database for the area, although many more are found in the analysis than are named in the available database. Further analysis shows that a richer interrogation of the landscape can be achieved with Geographical Information Systems when using this method than using standard approaches. key words fuzzy sets landforms morphometry multi-scale analysis mountains the Lake District

Delineation of Valleys and Valley Floors

“…In this paper, we are particularly interested in the delineation of landforms, that is to say attempts to answer questions such as "Where is a mountain?" posed by Fisher et al [2]. However, in our exploration of the literature we noted a concentration by GIScientists on the delineation of mountains (e.g.…”

“…These classification schemes havesometimes in adapted or extended form -often been applied to derive both crisp [25,26,27,28] and fuzzy [29,30] classifications. Wood [14] proposed multi-scale classification which was extended into fuzzy multi-scale classification based on a range of crisp classifications at different scales [2].…”

“…Fisher et al [2] present a partially top-down approach where they reason about the essence of peaks and their relationship to summits. They use fuzzy multi-scale classification into six morphometric classes resulting in fuzzy areas of peakness associated with summits.…”

“…Thus, our starting point is to characterise a landform of interest (e.g. a valley) before applying a range of methods to delineate the boundaries or, if we adopt a fuzzy approach similar to that proposed by Fisher et al [2], the valleyness of locations.…”

An Optimal and Practical Cache-Oblivious Algorithm for Computing Multiresolution Rasters

“…Fisher et al [4] use such a method in their landform classification algorithm; their algorithm constructs multiple rasters G µ , where a cell c of G µ covers the same region as µ × µ cells of the original fineresolution raster. The value assigned to c is equal to the average of the values of the original µ × µ cells.…”