Academic journal article Cartography and Geographic Information Science

Projecting Global Datasets to Achieve Equal Areas

Academic journal article Cartography and Geographic Information Science

Projecting Global Datasets to Achieve Equal Areas

Article excerpt

Introduction

Global modeling has become commonplace among scientists concerned with the environmental effects of human activities. Scientists routinely accomplish such modeling in the raster domain, using high resolutions for large parts of continents and low to high resolutions for the entire globe. Generally, low- to-moderate resolution datasets are 10-, 5-, or 1-degree cell size, and high-resolution datasets are 30-arc-second cells. Recent research has indicated that the transformation of such large areas through map projection equations and subsequent resampling leads to errors in statistical results tabulated from attributes of the transformed data (Steinwand et al., 1995; Usery and Seong 2001; Usery et al. 2002). A theoretical explanation of the transformation effects is given in Seong and Usery (2001), using some empirical data at the continental scale for Asia (Seong 1999). Kimerling (2002) developed a predictive model for the effects of pixel loss and duplication from transformations on equal-angular grids, and Seong et al. (2002) proposed the sinusoidal as one of the projections that reduce the problem. In Seong et al. (2002), errors were computed from a synthetic data matrix without the use of actual Earth surface datasets. Thus, only limited empirical work with real geographical data has been compiled tabulating the accuracy of total categorical areas in projected raster databases of global extent.

This paper is an attempt to fill the gaps in our knowledge concerning the empirical results of projection transformation of regional and global raster datasets. The goal of this research is not to generate absolute accuracy in the final projected datasets; rather, the goal is to assess the errors introduced in the transformation and resampling process. We do not assume that data in equal-angular grids are the most accurate or the best starting point for any given analysis. As Mulcahy (2000) indicates, data in equal-angular grids may include distortions arising from transformations of original sources. We simply wish to determine if projection transformation from equal-angular grids in spherical coordinates to a plane system and the required resampling introduce significant error in categorical areas, and if there are error patterns associated with various resolutions or particular projection selections. The empirical data for our analysis could have been simply resampled versions of data classified from satellite images. However, since the data exist in geographic coordinates in equal-angular cells, they provide a basis from which to empirically assess the errors introduced from projection transformation and resampling.

The next section of this paper details the empirical approach of comparing areas from spherical datasets in geographic coordinates with areas resulting after projection to a plane system. The third section provides descriptions of the datasets used and projections examined, and the fourth section discusses problems encountered in implementing the projection transformations in commercial software systems. The fifth section provides statistical analysis and graphical results. A final section draws conclusions from this work and provides some recommendations for the correct use of projection transformations and future research. Complete documentation of this research project and the datasets used are available at http://mciweb.er.usgs.gov/carto_research/projection/index.html.

Approach

Initially, we used available global datasets and commercial-off-the-shelf (COTS). software for projection transformation to determine the accuracy of areas. However, because of operational difficulties with COTS software, we include projection transformation results and analysis from an internal U.S. Geological Survey (USGS) software package for raster projection--Map Image or mapimg.

We have applied global area transformation and some regional transformations to a variety of datasets. …

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