Hydrologic Time Scale: A Fundamental Stream Characteristic

A new, fundamental catchment attribute called the hydrologic time scale τ governs the rate of delivery of runoff to a particular site, and is equal to $ \int {Q} dt/ \int|{d} {Q}|$, where Q is discharge and t is time. The value of τ for any gauged site is readily calculated from tabulated discharge data by replacing the integrals with sums. This quantity, coupled with the square root of catchment area, $ \sqrt{\mathit{A}} $, form a coordinate pair that embodies the characteristic time and length scales for any catchment, which govern its flow dynamics. The fitting constants used in several unit hydrograph models are simple multiples of τ, so knowledge of τ allows rapid calibration of these models for the particular site, facilitating flow prediction from rainfall data. Values of τ reflect many different landscape attributes, but for multiple sub-basins in watersheds with homogeneous land use and lithologic conditions, they correlate linearly with $ \sqrt{\mathit{A}} $. The ratio $ \sqrt{\mathit{A}}/\mathit{\tau } $ provides a characteristic velocity that is high for channelized, flood-prone rivers, for flashy urban streams with high impervious cover, and for sites downstream of hydropower dams. Sites with low velocities are resistant to flooding, as their landscapes have a greater ability to delay the delivery of runoff by retention, detention, and infiltration into the groundwater system.