Natural and anthropogenic influences on the scaling of discharge with drainage area for multiple watersheds

Discharge is the independent variable primarily responsible for shaping the hydraulic geometry and longitudinal profi le of rivers.The assumption is frequently made that discharge and drainage area scale linearly or nearly linearly, i.e., Q = kA c , where k is the theoretical discharge for a unit area watershed (A = 1), Q is river discharge (m 3 /s), A is drainage area (m 2 ), and c is the scaling power dependency.Watershed and longitudinal profi le modeling enjoy simplifi ed assumptions if discharge grows linearly with drainage area, and this assumption is widely applied.This paper investigates the scaling relationship between discharge and drainage area for fi ve large rivers, with an emphasis on exploring the linearity of the discharge-area relationship and suggesting causes for signifi cant departure from linearity.The fi ve large mainstem rivers explored (John Day, Salmon, Wabash, Greenbrier, and Yellowstone) all have a minimum of 60 years of continuous discharge records and have been selected to represent a wide geographic area spanning different land uses, climate, and topography.Peak annual fl ow and mean annual fl ow are compiled from the U.S. Geological Survey national surface-water database, and a linear regression analysis was completed for each year for the discharges.The fi ve rivers were selected to minimize, but not eliminate, the impacts of dams and diversions such as for irrigation on river discharges.The scaling factor (c) exhibits both secular and nonsecular trends over the length of record for these fi ve rivers.The results show that the studied watersheds can be grouped into two broad categories based on their respective c values: (1) those rivers where c is 1 or nearly 1, and (2) those rivers where c is signifi cantly <1.The John Day, Salmon, Wabash, and Greenbrier rivers scale at values of ~0.8 with natural variables including slope, elevation, and evapotranspiration potentially accounting for c values slightly <1.The second category is c values of ~0.5, as exhibited by the Yellowstone River.The Yellowstone watershed is unique for our study because of its secular trend, as well as its overall lower average c values.Climatic trends that control the timing of winter snowpack melting, increased frequency and intensity of forest fi res, and increased human consumptive water use in downstream areas may all contribute to the observed behavior in c for this watershed.The results from this set of rivers have broad implications for studies ranging from the modeling of fl uvial erosion in numeric landscape evolution models to allocations of water resources for human and environmental purposes.