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.     

Design and Implementation of a Model,Web-based,GIS-Enabled Cancer Atlas

Abstract

The design and development of a highly interactive web-based, GIS-enabled atlas is reported. The atlas is a prototype, designed as a model for implementation of atlases to support government cancer-control activities. This model integrates symbolisation and design principles from print cartography, interaction strategies from exploratory geovisualisation, and web-map/web-feature service advances from GIS. The atlas has been implemented using a client-server architecture. It makes use of two open-source GIS tools, PostGIS (as the system database) and GeoServer (to connect the database to the client mapping application). The client mapping application has been built in Macromedia Flash. The entire client-server architecture is described, then direct primary emphasis is focused on the client mapping application. For this component of the system, the interface design strategy is detailed, the approach taken to implement this strategy in Flash is documented, and the mechanisms developed to build dynamic links from the client to the underlying database through the server are outlined. Features of the atlas are presented through a prototypical use scenario for a target user.     

Multivariate Analysis and Geovisualization with an Integrated Geographic Knowledge Discovery Approach

The discovery, interpretation, and presentation of multivariate spatial patterns are important for scientific understanding of complex geographic problems. This research integrates computational, visual, and cartographic methods together to detect and visualize multivariate spatial patterns. The integrated approach is able to: (1) perform multivariate analysis, dimensional reduction, and data reduction (summarizing a large number of input data items in a moderate number of clusters) with the Self-Organizing Map (SOM); (2) encode the SOM result with a systematically designed color scheme; (3) visualize the multivariate patterns with a modified Parallel Coordinate Plot (PCP) display and a geographic map (GeoMap); and (4) support human interactions to explore and examine patterns. The research shows that such "mixed initiative" methods (computational and visual) can mitigate each other's weakness and collaboratively discover complex patterns in large geographic datasets, in an effective and efficient way.     

Retracing the Past: Recovering 19th Century Benchmarks to Measure Shoreline Change Along the Outer Shore of Cape Cod,Massachusetts

Between 1887 and 1888, Henry L. Marindin, Assistant Topographer of the U.S. Coast & Geodetic Survey, conducted a detailed survey of the outer shores of Cape Cod, Massachusetts, providing an important base line for future comparisons, “which will be of value to geologists and others who study the changes in the coast-line”. In 2007, the Land-Sea Interaction Program of the Provincetown Center for Coastal Studies began a project to resurvey Marindin's profiles and cross-sections to quantify changes to landforms and the nearshore environment that have occurred over the past century for use in estimating future conditions in the context of climate change and sea level rise. In order to facilitate reliable, quantitative shoreline comparisons, the translation of historical spatial data to contemporary horizontal (e.g., NAD83) and vertical (e.g., NAVD88) reference systems is paramount. With historical transects translated to NAD83 using methods developed as part of a previous study, the goal of this work is to develop an accurate estimate of the relationship between Marindin's elevation data and NAVD88. Recognizing that the physical and social landscape had changed significantly over the past 120+ years, a historical base map was prepared to assist with the recovery of 19th century benchmarks. Using the base map, five Coast survey benchmarks were recovered and resurveyed. Based on the results of this work, the local mean sea level datum of Marindin's survey is estimated to be 1.13 feet (0.34 meters) below the NAVD88 plane of reference.     

Bicomponent Trend Maps: A Multivariate Approach to Visualizing Geographic Time Series

The most straightforward approaches to temporal mapping cannot effectively illustrate all potentially significant aspects of spatio-temporal patterns across many regions and times. This paper introduces an alternative approach, bicomponent trend mapping, which employs a combination of principal component analysis and bivariate choropleth mapping to illustrate two distinct dimensions of long-term trend variations. The approach also employs a bicomponent trend matrix, a graphic that illustrates an array of typical trend types corresponding to different combinations of scores on two principal components. This matrix is useful not only as a legend for bicomponent trend maps but also as a general means of visualizing principal components. To demonstrate and assess the new approach, the paper focuses on the task of illustrating population trends from 1950 to 2000 in census tracts throughout major U.S. urban cores. In a single static display, bicomponent trend mapping is not able to depict as wide a variety of trend properties as some other multivariate mapping approaches, but it can make relationships among trend classes easier to interpret, and it offers some unique flexibility in classification that could be particularly useful in an interactive data exploration environment.     

Delaunay Triangulations and Stereographic Projections

After describing Delaunay triangulations of vertices on a sphere and in a plane, we prove that every Delaunay triangulation of vertices on a sphere corresponds to the Delaunay triangulation in the plane of any stereographic projection of the spherical triangle vertices. We then exploit this correspondence to build robust algorithms for Delaunay triangulations in the plane or on the sphere. We also describe a collection of "fisheye" conformal transformations of the sphere that are the composition of one stereographic projection with the inverse of another stereographic projection.     

The Exploratory Essays Initiative: Background and Overview

We define as Positional Accuracy Improvement the problem of putting together maps A and B of the same area, with B of higher planimetric accuracy. To do so, all objects in A might have to be slightly moved according to a mathematical transformation. Such transformation might ideally be of a specific type, like analytical or conformal functions. We have developed a theory to find a suitable analytical transformation despite it is not well defined because the only data available is the displacement vectors at a limited number of homologue control points. There exists a similar problem in fluid mechanics devoted on estimating the complete velocity field given just values at a limited number of points. We borrowed some ideas from there and introduced them into the positional accuracy improvement problem. We shall demonstrate that it is possible to numerically estimate an analytic function that resembles the given displacement at control points. As a byproduct, an uncertainty estimation is produced, which might help to detect regions of different lineage. The theory has been applied to rural 1:50.000 cartography of Uruguay while trying to diminish the discrepancies against GNSS readings. After the analytic transformation, the RMSE error diminished from 116 m to 48 m. Other problems with similar math requirements are the transformation between geodetic control networks.     

Using Semi-variance Image Texture Statistics to Model Population Densities

This study presents a method to model population densities by using image texture statistics of semi-variance. In a case study of the City of Austin, Texas, we first selected sample census blocks of the same land use to build population models by land use. Regression analyses were conducted to infer the relationship between block population densities and image texture statistics of the semi-variance. We then applied the population models to an area of 251 blocks to estimate populations for within-blocks land-use areas while maintaining census block populations. To assess the proposed method, the same analysis was performed while census block-group populations were maintained, and the aggregated block populations were compared with original census block populations. We also tested a conventional land-use-based dasymetric mapping method with pre-calculated population densities for land uses. The results show that our approach, which is based on initial land-use stratification and further image-texture statistical modeling of population, has higher accuracy statistics than the conventional land-use-based dasymetric mapping method.     

Opponent Process Theory and Syntax for Qualitative Relationships in Quantitative Series

Opponent Process theory is a model of human color perception that predicts that there are four unique hues, with all others appearing as mixtures. An experiment was conducted to evaluate this model for its ability to predict the perception of qualitative relationships in single-variable quantitative series. Two such series were tested—“Balance” schemes where the categories represent varying mixtures of two distinctly different phenomena, and “Bipolar” schemes where the series divides into halves of differing interpretation. The results indicate that Balance schemes were most often associated with part-spectral hue progressions that fell between unique hues, while Bipolar schemes were associated with hue progressions that crossed a unique hue. This effect however is apparent only when value relationships are “double-ended” within the series.     

Planetary Map Data Model for Geologic Mapping

Geologic mapping and the design of geologic (thematic) maps are nowadays supported by Geographic Information Systems (GIS). In order to gain a high degree of efficiency and to allow exchange of a common structured framework for mapping, map data models have been designed by agencies and individuals in order to support their mapping process. Only a limited number of such models are freely available and most of them are on a conceptual level. They support mappers in their work to define spatial geologic map units by integrating field and remote-sensing information and relate them to non-spatial information, in particular genetic surface types, rock composition, age and age relationships, attitude data, and other surface characteristics. All of these attributes are interrelated and require data models that depict these complex relationships without becoming too complicated for the mapper. Solutions on the basis of database management systems and server-client communication are highly efficient but they cannot be easily employed and require dedicated administration. A well-established alternative are file-based geodatabase concepts which are much more accessible but which also suffer from a number of limitations when it comes to administration and querying data.

The scope of this work is to find an accessible solution for working on and with geologic maps for planetary surfaces. We here present a planetary map data model (PMDM) design that has been implemented within Environmental Systems Research Institute's (ESRI) ArcGIS environment for systematic geologic and geomorphologic mapping of different planetary surfaces. The model copes with different genetic surface types, planetary stratigraphic systems, surface chronologies, specific naming conventions, and different body references. Additional and innovative assets are integrated solutions for semi-automated symbol assignments based on published standards (FGDC) and the possibility to perform topology checks on surface type features and units.