CONTROLS ON TRIBUTARY STREAM LENGTHS AS A FUNCTION OF MAINSTEM JUNCTION POSITION AND BASIN SHAPE

Understanding the controls on relief in landscapes is a fundamental goal of geomorphology. One commonly used relief metric is the elevation difference between a mainstem river channel and its adjacent ridges. For this metric, relief is sensitive to the length of tributary streams. As tributaries leave the mainstem, they gain elevation, meaning that longer tributaries generate more relief. Despite the importance of tributary length in creating relief, there does not exist theory or empirical rules for the controls on the length of tributaries within a watershed. This knowledge gap fundamentally limits our ability to predict the distribution of relief within a watershed. We hypothesize that moving downstream along the mainstem river from the divide to the outlet, the major tributaries of the mainstem river (defined here as tributaries that have a stream order number equal to or near that of the mainstream), will lengthen. To test this hypothesis we examined six steady state landscapes which represent over two orders of magnitude variation in uplift, over an order of magnitude variation in mean annual precipitation, and a large variation in lithology. Preliminary results show that, across all six landscapes, there exist a universal scaling, where tributary length linearly increases as the distance from the channel head increases. This relationship holds over variations in uplift, mean annual precipitation, and lithology, but the relationship is modulated by basin shape. Tributaries in basins with a more circular shape increase their length at a higher rate with downstream river distance than tributaries in more elongated basins. These results imply that relief between the mainstem and ridge should increase from the headwaters to the outlet, with the rate of change of relief to distance downstream being modulated by basin shape.