Testing the Linear Relationship Between Peak Annual River Discharge and Drainage Area Using Long-Term USGS River Gauging Records

River discharge is the fundamental process that operates in a fluvial system. The increase in discharge and drainage area downstream is intuitive, but data sets that describe this increase within individual watersheds are not common. The scaling of discharge and drainage area can be described as Q = kA c , where Q is river discharge, A is drainage area, and k and c are scaling constants. The variable k is not often illustrative of watershed processes, but the constant c represents the rate at which discharge (Q) increases downstream when compared to drainage area (A). This study compiles the annual peak discharge records of rivers from U.S. Geological Survey (USGS) gauges to determine the rate (c) at which discharge and drainage increase downstream. The peak annual discharge records were selected to represent a variety of watersheds spanning multiple climatic and geographic settings as well as to illustrate the effects of anthropogenic land-use change and river-management practices over the length of the records. It is often assumed that the scaling between discharge and drainage area is linear (c ~1), and 16 of these rivers exhibit this behavior over the length of their record. However, most of the rivers studied show nonlinear behavior and/or secular trends in their c values. Eleven rivers have peak annual discharge scaling values (c) of \u3c1, three have c values substantially larger than 1, and ten exhibit secular changes in c over part or all of their records. These nonlinear and changing c values can be attributed to both natural and anthropogenic causes, such as dams, urbanization, and other land-use changes. These c values indicate the need for caution before assuming that discharge and drainage area are linearly related