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

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.