CaGIS Vol. 29, no. 2

A Graphical Method for Exploring Spatiotemporal Point Distributions

Yukio Sadahiro

ABSTRACT: A spatiotemporal point distribution is a set of points defined by the combination of a spatial region and a time period. It is used for representing a set of discrete events, such as traffic accidents, and a set of points that characterize line and polygon objects such as the turning points of insect movement. Analysis of a spatiotemporal point distribution is more difficult than an ordinary spatial point distribution because it has to be treated in a three- or four-dimensional spatiotemporal region, where data visualization and analysis have not been fully explored. This paper proposes a new method for representing the spatiotemporal point distribution, which is useful for exploratory analysis. The method summarizes the information extracted from the point distribution, and thus helps us find important and interesting patterns in the distribution. It consists of two steps: conversion of a spatiotemporal point distribution into a surface, and graphic representation of the surface. Along with a theoretical description of the method, technical details including a computational algorithm are discussed. To test the validity of the method, an expansion of convenience stores in Tokyo, Japan, is analyzed.

KEYWORDS: Graphical representation, exploratory analysis, spatiotemporal point distribution, peak diagram

Interactivity Types in Geographic Visualization

Jeremy W. Crampton

ABSTRACT: This paper introduces and discusses types of interactivity that can be used in digital mapping environments. The interactivity types are placed in the framework of geographic visualization (GVis) in order to extend the GVis emphasis on exploratory, interactive and private functions of spatial displays. After defining interactivity in general, four categories of interactivity are proposed: with (1) the Data; (2) the Data Representation; (3) the Temporal Dimension; and (4) Contextualizing Interaction. Three benefits of this typology are discussed. First, interactivity types can be combined to build an interactive environment. More powerful interactive mapping environments not only employ more interactivity types, but combine types from different categories. Second, the typology allows cartographers to compare and critique different mapping and GIS environments and gives cartography educators and students a mechanism for understanding the different types of interactivity, as well as a set of concepts for imagining and creating new interactive environments. Third, a typology of interactivity gives interface designers a mechanism with which to identify needs and measure interface effectiveness. In order to examine these issues in practice, two common interactive mapping environments are briefly examined to determine the interactivity types employed, and a measurable difference of interactive potential is obtained.

KEYWORDS: Interactivity, typology, geovisualization

Artificial Neural Networks as a Method of Spatial Interpolation for Digital Elevation Models

David A. Merwin, Robert G. Cromley, and Daniel L. Civco

ABSTRACT: This paper examines the performance of artificial neural networks (ANNs) as a method of spatial interpolation, when presented with irregular and regular samples of elevation data. The results of the ANN interpolation are compared with results obtained by kriging. Tests of spatial bias in the systematic errors contained in each of the neural network-derived DEMs were conducted using four attributes: slope, aspect, average direction and average distance from the nearest sampled value. Based on RMS and other evaluation measures, the accuracy of estimated DEMs from regular and irregular sample distributions using neural networks is lower than the accuracy level derived from kriging. The accuracy level of the ANN interpolators also decreases as the range of elevation values in DEMs increases. As reported in the literature, ANNs are approximate interpolators, and the pattern of under-prediction and over-prediction of elevation values in this study revealed that all estimated values fell within the range of sample elevations. Neural networks cannot predict values outside the range of elevation values contained in the sample, a property shared by other interpolators such as inverse weighted distance.

KEYWORDS: Spatial interpolation, artificial neural networks (ANN), digital elevation model (DEM)

Predicting Data Loss and Duplication when Resampling from Equal-Angle Grids

1. Jon Kimerling

ABSTRACT: Global data sets for elevation and other environmental phenomena are commonly distributed as “equal-angle” grids with cell edges defined by equal angular increments of latitude and longitude (quadrilateral cells). Equal-angle grids of varying spatial resolution are the primary data source for small-scale maps of global or continental extent produced as scientific or commercial products. Nearest-neighbor resampling of grid data is commonly employed to create maps on a variety of projection surfaces, but little attention has been paid to the loss and duplication of data in the equal angle grid that is a consequence of the resampling process. This paper focuses on the creation and use of what is termed a Data Loss and Duplication Map (DLDM) as an essential tool for understanding the spatial and mathematical nature of data loss and duplication during resampling. DLDMs corresponding in spatial resolution to the ETOPO5 global elevation data set were created for the cylindrical equal area, sinusoidal, and Lambert azimuthal equal-area world map projections. Each DLDM not only allowed the global pattern of data loss and duplication to be visualized, but also provided data for graphs showing the extent of loss and duplication at five-minute latitude and longitude intervals. These graphs proved essential to deriving equations for each projection that predict the extent and location of data loss and duplication on the DLDM and hence in the ETOPO5 data set.

KEYWORDS: Equal-angle global grids; nearest-neighbor resampling; data loss and duplication map; resampling error.