Can stream junction angles reliably predict slope and area relationships of branched channel networks?

The angular relationship by which steeper, lower-order streams join higher-order mainstems at an acute angle in the upstream direction has been recognized since the emergence of geomorphology. A geometric construction posited by Howard (1971) attempts to explain this relationship, whereby stream junction angle correlates with the ratio of mainstem to tributary gradient ( cos(z) = S ms /S tr ). In this study, we test this geometric construction by measuring stream junction angles, gradient ratios, and contributing watershed area from moderate resolution digital topography (5 and 10 m), and compare these results to Howard's hypothesis. Three separate drainages highlighted by previous work from Howard (1971) were selected from the Mt. Ellen 2NW (Utah), Los Olivos (California), and Hyden West (Kentucky) 7.5 minute quadrangles as example networks with very small (<30°, Mt. Ellen) to large junction angles (>70°, Hyden West) to test this model. In all three cases, there is no correlation between stream junction angles and either gradient ratios or watershed areas. It is unclear whether gradient ratios are obfuscated by data noise, but, interestingly, stream intersections with higher gradients from the large junction angle dataset have high correlation coefficients (0.94). However, when watershed area is transformed by local channel concavity, a metric that is less susceptible to data noise, there is no correlation between stream junction angles and transformed relative watershed area. These results may highlight the limitations of using simple geometric construction to characterize branched channel networks where factors such as variable local concavity in non-equilibrium drainages may introduce complications. We speculate that the drainages highlighted by Howard (1971) could instead represent an evolutionary trend towards steady-state conditions whereby acute stream junction angle landscapes represent initial conditions of an incipient, undissected landscape. By contrast, a mature landscape with larger junction angles would represent an approach to steady-state that overprints the initial condition of an undissected landscape.