CaGIS vol. 31, no. 2

Hillshading of Terrain Using Layer Tints with Aspect-Variant Luminosity

Patrick J. Kennelly and A. Jon Kimerling

Hillshading provides a rendering of topographic surfaces by assigning brightness to surface elements based on the orientation of these elements and a selected direction of illumination. Users easily visualize many topographic features, but some areas lack detail, as one shade of gray does not define a unique surface orientation. We clarify some of this ambiguity by varying the color of layer tints with aspect direction. We use the CIELAB color model to quantify color specifications and map variations in luminosity onto slices of the Hue-Saturation-Value (HSV) color model. Traditionally, cartographers assign an aspect-invariant color (or colors) based on H and S and vary V with the hillshading values. In our research, we assign aspect-variant H and V values in close proximity in HSV color space. We use values of luminosity and saturation from the CIELAB and HSV color models to select colors that are least saturated, most saturated, least luminous, and most luminous to represent the northwest, southeast, southwest, and northeast directions, respectively. We then vary V in the traditional manner with hillshading from the northwest. Topographic details not apparent in the original hillshaded maps are highlighted with this technique.

KEYWORDS: Analytical hillshading, aspect, Hue-Saturation-Value (HSV) color model, Commission International de l’Êclairage (CIELAB) color model, luminosity

Numerical Evaluation of the Robinson Projection

Cengizhan Ipbuker

The Robinson projection is one of the most preferred projections for world reference maps in atlas cartography. The projection is constructed from Robinson’s look-up table since there are no analytical formulas. This deficiency has led to a number of requests for the plotting formulas to which cartographers have responded by deriving analytical equations using different interpolation algorithms applied to Robinson’s table values. The Robinson projection was examined with regard to its deformations calculated by four different algorithms, including the multiquadratic method. The numerical evaluations were then used to compare the algorithms. Solutions have been presented including some criticisms about this projection. The latitudes along which the scale is true and on which the maximum angular distortion equals zero have been determined.

KEYWORDS: Robinson projection, cubic spline interpolation, multiquadric interpolation

Toward a Differential Calculus for Temporal Map Analysis

Denis J. Dean

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.

KEYWORDS: Spatio-temporal analysis, differential calculus, rates of change, interpolation, degrees of freedom

Dasymetric Estimation of Population Density and Areal Interpolation of Census Data

James B. Holt, C. P. Lo, and Thomas W. Hodler

This paper describes techniques to compute and map dasymetric population densities and to areally interpolate census data using dasymetrically derived population weights. These techniques are demonstrated with 1980-2000 census data from the 13-county Atlanta metropolitan area. Land-use/land-cover data derived from remotely sensed satellite imagery were used to determine the areal extent of populated areas, which in turn served as the denominator for dasymetric population density computations at the census tract level. The dasymetric method accounts for the spatial distribution of population within administrative areas, yielding more precise population density estimates than the choroplethic method, while graphically representing the geographic distribution of populations. In order to areally interpolate census data from one set of census tract boundaries to another, the percentages of populated areas affected by boundary changes in each affected tract were used as adjustment weights for census data at the census tract level, where census tract boundary shifts made temporal data comparisons difficult. This method of areal interpolation made it possible to represent three years of census data (1980, 1990, and 2000) in one set of common census tracts (1990). Accuracy assessment of the dasymetrically derived adjustment weights indicated a satisfactory level of accuracy. Dasymetrically derived areal interpolation weights can be applied to any type of geographic boundary re-aggregation, such as from census tracts to zip code tabulation areas, from census tracts to local school districts, from zip code areas to telephone exchange prefix areas, and for electoral redistricting.

Book Review

Political Ecology: An Integrative Approach to Geography and Environment-Development Studies (2003), Karl S. Zimmerer and Thomas J. Bassett (eds). The Guilford Press, New York. ISBN: 1572309164. Paperback, $27. Reviewed by Salvatore Engel-Di Mauro, University of Wisconsin.