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

Abstract

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.

Analysing river network dynamics and active length - discharge relationship using water presence sensors

“…To correct the asynchronicity between the electrical signals recorded by the sensors and the persistencies of the corresponding nodes, the model developed by (Durighetto et al, 2020;Botter and Durighetto, 2020;Durighetto and Botter, 2021 (in press) was applied. It links the spatial configuration of the network to weather data and here it was applied to estimate the persistency of the nodes between the 4 th of September and the 24 th of October 2019 knowing rainfall heights of that same period as well as persistencies and precipitation data collected between July 2018 and January 2019 used to develop the model (Figure C1).…”

“…The latter was calculated as the fraction of time during which a node was simulated as active in the reference period (September and October of 2019). Previous studies have indicated that the model is able to accurately reproduce the observed spatial patterns of persistency in the study catchment under different hydrological conditions (Durighetto et al, 2020;Botter and Durighetto, 2020).…”

“…This suggests that the statistics of the ER signals recorded in the field could be robust indicators of the hydrological status of different network nodes. In particular, ER time series could be used to extrapolate information on the spatial patterns of node persistency, which could be in turn used to define the hierarchy according to which the nodes in the network are activated in response to rain events and then deactivated during the subsequent drying (Botter and Durighetto, 2020).…”

Variability of stream extents controlled by flow regime and network hydraulic scaling

“…We present timeseries of Q and L of representative years for each site, as well as exceedance probability plots for the entire timeseries of record. The exceedance probability of L is equivalent to one minus the stream length duration curve recently described by Botter and Durighetto (2020), although that study specifically focuses on reaches with flowing water rather than wetted extents that may or may not exhibit clear flow.…”

“…Temporal variability in L has been considered using flow duration curves combined with L ( Q ) (e.g., Jensen et al, 2017), and time series plots of L have appeared in the literature, either as individual point observations (e.g., Blyth & Rodda, 1973; L. D. Day et al, 1987; Durighetto et al, 2020), or via extrapolation by fitting a functional form between L and Q (e.g., Zimmer & McGlynn, 2017) Datry et al (2007) summarized time variation in L for two small catchments using the coefficient of variation ( CV L ), equal to the standard deviation of L divided by its mean. Botter and Durighetto (2020) explored how the persistency and spatial distribution of nodes within the channel network impact the stream length duration curve using a stochastic model; their framework allows for estimating average persistency and variation of a network where spatially explicit data are available. However, a framework unifying the role of β and Q as drivers of variability in L is lacking.…”