Abstract
Rivers form characteristic branching patterns as they drain landscapes. Past work has shown that the angles formed between confluent channels at river junctions vary with climate aridity-but why this occurs is contested. We show how this climate sensitivity can be explained by the principle that river networks self-organize toward "optimal" configurations that minimize the hydraulic expenditure of energy. Starting from this energy minimization principle, optimal junction configurations can be calculated given three variables: the drainage area ratio of confluent channels, the scaling exponent relating channel gradient to drainage area (often called the concavity index), and the scaling exponent relating discharge to drainage area. Given that concavity and discharge-drainage area scaling vary with climate aridity, optimal junction angle theory can explain junction angle climate sensitivity. We extracted a global dataset of approximately 26 million junctions and show that the predictions of the optimal junction model are consistent with the sensitivity of junction angles to climate aridity. Our dataset includes not only the junction angle between confluent tributaries but also the "bending angles" between each tributary and the downstream channel, enabling us to quantify junction symmetry. As in the model, the geometric symmetry of real junctions is strongly controlled by the discharge ratio of the confluent channels. However, junctions with strongly asymmetric tributary drainage areas do not exhibit optimal geometries: minor tributaries show a tendency to join large rivers at the outside apex of large-scale bends.