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

Abstract

Stream networks expand and contract through time, impacting chemical export, aquatic ecosystem habitat, and water quality. Although recent advances improve prediction of the extent of the wetted channel network (L) based on discharge at the catchment outlet (Q), controls on the temporal variability of L remain poorly understood and unquantified. Here we develop a quantitative, conceptual framework to explore how flow regime and stream network hydraulic scaling factors co-determine the relative temporal variability in L. Network hydraulic scaling determines how much L changes for a change in Q, while the flow regime describes how Q changes in time. We compiled datasets of co-located dynamic stream extent mapping and discharge to analyze all globally available empirical data using the presented framework. We found that although variability in L is universally dampened relative to variability in Q (i.e., streamflow is relatively more variable in time than network extent), the relationship is elastic, meaning that for a given increase in the variability in Q, headwater catchments will experience greater-than-proportional increases in the variability of L. Thus, under anticipated climatic shifts towards more volatile precipitation, relative variability in headwater stream network extents can be expected to increase even more than the relative variability of discharge itself. Comparison between network extents inferred from the L-Q relationship and USGS topographic maps shows widespread underestimation of the wetted channel network by the mapped extent of both perennial and dynamic stream extents.

On the Relation Between Active Network Length and Catchment Discharge

“…This key analytical result explains how and why morphologic and geolithologic catchment features lie at the basis of the link between L and Q (as foreseen by Prancevic and Kirchner (2019)), while climate does not produce any direct signature on the shape of active length ‐ discharge relationship, though being directly involved in the dynamics of both L and Q (as suggested by Lapides et al. (2021), and shown in Figures 3b, 3d and 3e).…”

“…The standard analytical model used to interpret the relationship between active length and catchment discharge is the power law model, first introduced by Gregory and Walling (1968) and then widely adopted in the literature of temporary streams (Blyth & Rodda, 1973; Day, 1978; Durighetto et al., 2022; Godsey & Kirchner, 2014; Jensen et al., 2017; Lapides et al., 2021; Prancevic & Kirchner, 2019; Senatore et al., 2020; Shaw et al., 2017; Ward et al., 2018; Zanetti et al., 2021; Zimmer & McGlynn, 2017). The power law model, however, tends to infinity when $$Q\to \infty $$ with a speed which is impacted also by the lower values of L and Q , and thus it might not capture cases in which the L ( Q ) law has an horizontal plateau, for example, because the channel heads can’t move upstream beyond a given point due to morphological constraints (see Figure 4, SI and Jensen et al.…”

“…In the proposed perceptual model, the presence/absence of surface flow at a given location is represented by the local status of the focus stream portion: $$$X(x,t)=\left\{\begin{array}{cc}\hfill 1\hfill & \hfill \text{if}\,Q(x,t) > {Q}^{\ast }(x)\hfill \\ \hfill 0\hfill & \hfill \text{otherwise}\hfill \end{array}\right.,$$$ where X = 1 implies the presence of flowing water and X = 0 corresponds to a dry section (Botter & Durighetto, 2020). In the above equation, the subsurface transport capacity Q *( x ) usually refers to fully‐saturated conditions and is a durable feature of each location of the study catchment determined by stationary hydro‐morphological properties (e.g., saturated hydraulic conductivity, topographic gradient, transmissivity) (Lapides et al., 2021; Prancevic & Kirchner, 2019). The water flow supplied from upstream Q ( x , t ), instead, varies both in space and time.…”

“…The link between the actively flowing length of a stream network ( L ) and the discharge at the corresponding outlet ( Q ) has long been studied in the hydrological literature (Blyth & Rodda, 1973; Day, 1978; Gregory & Walling, 1968). Empirical L ( Q ) relations have been used to quantify the sensitivity of the active length of streams to changes in the underlying hydrological conditions in selected case studies (Durighetto et al., 2022; Godsey & Kirchner, 2014; Jensen et al., 2017; Lapides et al., 2021; Prancevic & Kirchner, 2019; Senatore et al., 2020; Shaw et al., 2017; Ward et al., 2018; Zanetti et al., 2021; Zimmer & McGlynn, 2017). However, owing to the operational burden associated to river network mapping, to date the dynamics of wet length has been measured only in relatively few catchments.…”

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

“…Supporting code is available on GitHub (https://zenodo.org/record/4057320; Leclerc et al, 2020a). A preprint of this study is available in the public domain (Lapides et al, 2020).…”