Cartographic and Geometric Components of a Global Sampling Design for Environmental Monitoring

A comprehensive environmental monitoring program based on a sound statistical design is necessary to provide estimates of the status of, and changes or trends in, the condition of ecological resources. A sampling design based upon a systematic grid can adequately assess the condition of many types of resources and retain flexibility for addressing new issues as they arise. The randomization of this grid requires that it be regular and retain equal-area cells when projected on the surface of the earth. After review of existing approaches to constructing regular subdivisions of the earth's surface, we propose the development of the sampling grid on the Lambert azimuthal equal-area map projection of the earth's surface to the face of a truncated icosahedron fit to the globe. This geometric model has less deviation in area when subdivided as a spherical tessellation than any of the spherical Platonic solids, and less distortion in shape over the extent of a face when used for a projection surface by the Lambert azimuthal projection. A hexagon face of the truncated icosahedron covers the entire conterminous United States, and can be decomposed into a triangular grid at an appropriate density for sampling. The geometry of the triangular grid provides for varying the density, and points on the grid can be addressed in several ways.