Application of the Radical Law in Generalization of National Hydrography Data for Multiscale Mapping

The importance of automating feature generalization is increasing in conjunction with demands for updated data. Determining which features to represent at myriad scales is an important part of this process. The Principles of Selection, as proposed by Töpfer and Pillewizer in 1966, provide cartographers with an empirically based generalization rule. Also known as the Radical Law, the principles provide an equation estimating the number of features depicted at smaller scales based on the relationship of map scale denominators. However, the applicability of the equation at large scales seems limited in its current form. With ongoing initiatives to automate cartographic processing and the digitization of data at large scales, there is utility in determining how many features to display on derived medium and small scale products. We evaluate the USGS National Hydrography Dataset and National Atlas hydrography to determine the existing length of features for comparison to expected results based on the Radical Law equation. The rate of feature selection is not the same along the continuum of scale. A new factor is added to the Radical Law equation to account for this variability. Results from a USGS flowline pruning tool by Stanislawski and Buttenfield are used to compare equation results to benchmark USGS hydrography at 5K, 24K, 100K and 2M scales. Increasing knowledge of existing hydrographic features can improve implementation of automated feature generalization and propagation through a wide range of scales.