Stream Network Dynamics and the Geometry of Off-Channel Pathways: An Analytical Approach

River networks undergo changes over time that manifest as expansions and contractions. As a consequence of these changes, the distances between hillslope source areas and flowing channels change. To adequately describe this phenomenon, it is necessary to formulate an analytical mathematical model capable of decoupling the magnitude of the impact caused by changes in the active network from how this impact is redistributed among off-network paths of different lengths. To this aim, an analytical framework termed Flowpath-Length Selection (FLS) is developed, which describes how the off-network length distribution evolves with ac tive network length. The starting point is a conservation equation for the off-network length probability density, from which the network impact is decomposed into a mean component, which controls the magnitude of the average change in off-network lengths, and a rank-based selection component, which accounts for the distribution of this impact across flowpath-length ranks. The two components are modeled separately: the mean impact is represented by a geomorphic model based on the network-length–pruning-area scaling, while the selection is described by a power-law FLS parameterization dependent on the normalized active-channel length. The model formulation yields an analytical solution in quantile space for the evolving off-network length distributions. Testing the model across multiple catchments reveals two remarkable features: the mean impact per unit change in active-network length decreases as the network expands, while longer flowpaths are preferentially impacted by network dynam ics, with this preference becoming increasingly pronounced as the active network expands. A single parameterization shared across all the basins studied is capable of reproducing, to a large extent, the general dynamics of the distributions in response to changes in the ac tive network, with a relative error of 0.050, while basin-specific calibrations introduce further localized improvements. Separating the two components that govern the impact of active net work dynamics allows them to be modeled independently; they also provide a basis for more complex formulations capable of representing general network expansions and contractions and for future developments concerning catchment response times.