Sub‐Grid‐Scale Characterization of Channel Lengths for Use in Catchment Modeling

We explored methods for extrapolating mainstream channel lengths of first‐order drainage basins from synoptic data to characterize them for numerical watershed modeling. We analyzed four catchments in a climatologically semiarid arid geologically homogeneous region east of the Cascade Mountains in Washington state. Within each of these catchments, we identified stream channel networks manually from 1:24,000‐scale topographic maps, and from 50‐m resolution digital elevation models using commercially available drainage network extraction methods. A least squares fit of logarithms of mainstream length plotted against basin area established a regression relation to use for predicting mainstream lengths in the smallest subbasins. To test our relation, we compared predicted mainstream lengths with first‐, second‐ and third‐order channel lengths measured from low‐altitude aerial photographs of a representative fourth‐order basin. Our results indicate that relations of mainstream length to basin area derived from coarsely gridded data (e.g., 30 m) cannot be used to characterize stream and basin morphometry in the smallest basins due to the presence of hydrologic and geometric controls (i.e., thresholds) that limit the mainstream channel length and total basin length in first‐, second‐, and third‐order basins. The presence of these thresholds potentially constrains the range over which theoretically self‐similar, or fractal, relationships can be applied to stream‐channel networks.