On the Relation Between Active Network Length and Catchment Discharge

The ever-changing hydroclimatic conditions of the landscape induce ceaseless variations in the wet channel length (L) and the streamflow (Q) of a catchment. Here we use a perceptual model to analyze the links among (and the drivers of) four descriptors commonly used to characterize discharge and active length dynamics in streams, namely the L(Q) relationship and the cumulative distributions of local persistency, flowrate and active length. The model demonstrates that the shape of the L(Q) law is defined by the cumulative distribution of the specific subsurface discharge capacity along the network, a finding which provides a clue for the parametrization of L(Q) relations in dynamic streams. Furthermore, we show that L(Q) laws can be constructed combining the streamflow distribution with disjoint active length data. Our framework links previously unconnected formulations for characterizing stream network dynamics, and offers a novel perspective to describe the scaling between wet length and discharge in rivers.Plain Language Summary Stream networks react to changing climatic conditions (wetting or drying) in the surrounding landscape. Consequently, the length of flowing channels and the corresponding streamflow vary through time owing to precipitation events and seasonal climatic patterns. Here we present a conceptual model that analyzes the controlling factors of four standard descriptors of streamflow and active length dynamics in streams, and identifies their mutual connections. The model provides insight on the physical processes that determine the joint changes of active length and discharge, investigating the impact of climate and landscape morphology on these standard descriptors. The approach formally describes how the relation between flowrate and active length originates from the spatial aggregation of local properties of the stream network (water supply and transport capacity). A set of mathematical relations is also derived, which can be used in practical applications to interpret and predict the relationship between wet length and catchment discharge - even in cases in which synchronous measurements of these two variables are not available.