On the Spatial Distribution and Geologic Controls of Fractal Catchment Morphometry in the Continental United States

Fractal analysis in the context of basin morphometry provides a me ans to quantify the signature of dynamic surface processes which inform basin development and their interactions with the geologic materials and structures upon which they act. This study seeks to quantify this signature and its distribution throughout the United States, a nd establish its relationship with the basin's interior geomorphology.

A two-dimensional box counting algorithm was applied to 14,948 standard HUC8 basins in the continental United States in order to provide a box-counting dimension, an indicator of fractal dimension (FD) . Hypsometric integrals (HI) were also calculated for all basins using 100m DEM data. This data was spatially organized using GIS software and subject to Getis-Ord G* cluster analysis to identify significant spatial distributions of high and low FD values.

F Ds for the majority of basins were found to be between 1.0 1 and 1.13, with a Gaussian distribution from their mean value of 1.06. The low error provided by the box counting algorithm ( ± 0.01) provided the resolution necessary to identify clusters of high and low fractal dimension values centered on various geologic controls and physiographic regions (Figure 1) . Getis-Ord G* clusters statistically confirmed these relationships. HI data indicates that low fractal dimension basins tend to correlate with a greater degree of spatial clustering in HI values, and vice-versa for high FD basins.

There exist s a significant discrepancy in FD value between the eastern and western United States, with the East being dominated by high FD values with the exception of certain provinces of the Appalachians, and West being dominated by low FD values, particularly in regions exhibiting a high degree of structural control or areas with particularly high or low HIs, indicating a landscape at disequilibrium.

This seems to imply a relationship between the development of catchment form and the degree to which the interior of a basin has been allowed to self organize into a steady-state. These results could provide a valuable window into the dynamics of basin development when viewed as a dynamical system, as well as a metric with a high degree of persistence that is tied to the general organizational pattern of a basin's interior as opposed to a specific static configuration.