The Stream Length Duration Curve: A Tool for Characterizing the Time Variability of the Flowing Stream Length

In spite of the importance of stream network dynamics for hydrology, ecology, and biogeochemistry, there is limited availability of analytical tools suitable for characterizing the temporal variability of the active fraction of river networks. To fill this gap, we introduce the concept of Stream Length Duration Curve (SLDC), the inverse of the exceedance probability of the total length of active streams. SLDCs summarize efficiently the effect of hydrological variability on the length of the flowing streams under a variety of settings. A set of stochastic network models is developed to link the features of the local hydrological status of the network nodes with the shape of the SLDC. We show that the mean network length is dictated by the mean persistency of the nodes, whereas the shape of the SLDC is driven by the spatial distribution of the local persistencies and their network-scale spatial correlation. Ten field surveys performed in 2018 were used to estimate the empirical SLDC of the Valfredda river (Italy), which was found to be steep and regular—indicating a pronounced sensitivity of the active stream length to the underlying hydrological conditions. Available observations also suggest that the activation of temporary reaches during network expansion is hierarchical, from the most to the least persistent stretches. Under these circumstances, the SLDC corresponds to the spatial Cumulative Distribution Function of the nodes persistencies. The study provides a sound theoretical basis for the analyses of network dynamics in temporary rivers.