Rate-of-Change Maps

Mapping spatial change is a fundamental theme in geography. The analytical and numerical application of differential calculus to continuous geographic data produces first-derivative distributions that can be mapped to show gradient magnitude and gradient direction, and second-derivative measures that can be mapped to show the form (convexity, concavity) of the geographic surface. When these differential measures are obtained for spatially distributed temporal data, a velocity/acceleration change map can be constructed. Cartographic applications of the methodology presented in this paper include slope and curvature landform mapping, derivative trend-surface mapping of urban housing value gradients and the velocity/acceleration mapping of mobile-home residency in the United States from 1950 to 1980.     

Toward a Differential Calculus for Temporal Map Analysis

Investigators in many fields are analyzing temporal change in spatial data. Such analyses are typically conducted by comparing the value of some metric (e. g., area, contagion, or diversity indices) measured at time T₁ with the value of the same metric measured at time T₂ . These comparisons typically include the use of simple interpolation models to estimate the value of the metric of interest at points in time between observations, followed by applications of differential calculus to investigate the rates at which the metric is changing. Unfortunately, these techniques treat the values of the metrics being analyzed as if they were observed values, when in fact the metrics are derived from more fundamental spatial data. The consequence of treating metrics as observed values is a significant reduction in the degrees of freedom in spatial change over time. This results in an oversimplified view of spatio-temporal change. A more accurate view can be produced by (1) applying temporal interpolation models to observed spatial data rather than derived spatial metrics; (2) expanding the metric of interest's computational equation by replacing the terms relating to the observed spatial data with their temporal interpolation equations; and (3) differentiating the expanded computational equation. This alternative, three-step spatio-temporal analysis technique will be described and justified. The alternative technique will be compared to the conventional approach using common metrics and a sample data set.     

Adapting Generalization Tools to Physiographic Diversity for the United States National Hydrography Dataset

This paper reports on generalization and data modeling to create reduced scale versions of the National Hydrographic Dataset (NHD) for dissemination through The National Map, the primary data delivery portal for USGS. Our approach distinguishes local differences in physiographic factors, to demonstrate that knowledge about varying terrain (mountainous, hilly or flat) and varying climate (dry or humid) can support decisions about algorithms, parameters, and processing sequences to create generalized, smaller scale data versions which preserve distinct hydrographic patterns in these regions. We work with multiple subbasins of the NHD that provide a range of terrain and climate characteristics. Specifically tailored generalization sequences are used to create simplified versions of the high resolution data, which was compiled for 1:24,000 scale mapping. Results are evaluated cartographically and metrically against a medium resolution benchmark version compiled for 1:100,000, developing coefficients of linear and areal correspondence.     

Multiparametric Cartographic Visualisation of Glacier Rheology

Abstract

In cooperation between remote sensing experts and cartographers interested in glaciology, new types of maps showing the glacier dynamics have been developed. The maps make use of the original phase gradient approach to glacier rheology modelling based on repeat-pass ERTS SAR interferograms. Careful map design and, in particular, colour assignment allow the visualisation of the glacier dynamics in its locally changing velocity with an estimated accuracy of approximately 2.0 cm per day. Two map derivates – a differential interferogram showing the glacier velocity and another product displaying the glacier strain rate – have been designed. Moreover, maps displaying the glacier marginal changes within the space of four years have been generated. The strain rate maps evidence that spots with high values frequently correspond with crevasse-prone areas which are even detectable under thick layers of snow. In this sense, the latter visualisations can be seen as maps of crevasse danger zones. The Svartisen in Norway and the Hintereis Glacier in Austria served as testbeds for the development of these different types of maps which are at the scales of 1:25 000, 1:50 000 and 1:100 000.     

MacLeod,MI4, and the Directorate of Military Survey 1919–1943

Abstract

The organization lineage of the UK Defence Geographic and Imagery Intelligence Agency can be traced back to the seventeenth century. For much of this time the organization, bearing a succession of different titles, formed only a very small section of the armed forces, and, until the World War of 1914–1918, its main duties were the creation and maintenance of a map collection and the acquisition of geographical data of foreign countries. The survey and mapping innovations made during the war greatly enlarged the remit of what was now termed the Geographical Section General Staff (MI4). This paper outlines the work of MI4 in the inter-war years taking account of the principal personalities involved, and traces the controversial background to the creation in 1943 of the Directorate of Military Survey — the immediate predecessor of the DGIA.     

Complex Coastline Generalization

A combination of procedural algorithms and predicate logic formalisms is proposed to generalize complex coastlines. The advantage of this combined strategy is to cover both the geometric and conceptual aspects of the generalization process. The geometric part is dedicated to simplification and displacement operations for graphical presentation. The conceptual part handles the problem of river selection based on geometrical and semantic criteria. The derivation of a hierarchical model reflecting the hierarchical structure of the bay/river network of the coastline is a requirement for river selection. A case study was carried out, and results show an improvement over more conventional procedural approaches. The idea of building a hierarchical model to prepare the ground for feature selection can be applied to other hierarchically structured objects such as road networks or nested buildings in urban areas.