Growing mountain ranges and quenched river networks

River networks in mountain ranges owe their existence to the competing effects of tectonic uplift and climate-controlled erosion. However, paradoxically, the universal geometric properties of river networks are independent of both tectonics and climate. Currently, this paradox has still not been resolved. Here we propose a solution that consists in considering that the geometry of river networks is established on the lowland margins of incipient uplifts, and is quenched into the erosion zone as the mountain belts widen with time. In our model, the geometry of river networks simply reflects the downward coalescence of alluvial rivers on undissected surfaces outside of mountain belts, and is therefore independent of erosion processes.