Flowing stream networks extend and retract seasonally and during rainfall events (Ågren et al., 2015; Day, 1978; Gregory and Walling, 1968; Jensen et al., 2017; Peirce and Lindsay, 2015; Shaw, 2016). Some networks are less dynamic than others, depending on their geological and topographic settings (e.g., Whiting and Godsey, 2016), but many stream networks that are not strongly controlled by persistent springs expand dramatically with increasing wetness conditions and streamflow. For example, the length of the flowing stream network in Sagehen Creek in California was 35 km during wet conditions in April 2008 but only 15 km during dry conditions in September 2006 (Godsey and Kirchner, 2014). The flowing stream drainage density of the completely extended stream network for a British peatland catchment was 20 times greater than that of the fully retracted stream network (Goulsbra et al., 2014). In an agricultural catchment in Oregon the flowing drainage density increased by 2 orders of magnitude between dry summer periods and wet winter periods (Wigington et al., 2005).

The expansion of the flowing stream network during wet periods increases the connectivity between hillslopes and streams. Wigington et al. (2005) argued that this increase in connectivity leads to higher nitrate exports because riparian buffer strips are largely bypassed, and travel times are shorter, when the flowing stream network is fully extended. Yet most catchment-scale solute transport studies assume static drainage networks, often derived from topographic maps that do not adequately represent intermittent streams. Even when intermittent streams are delineated as dashed lines on maps, their abundance is often greatly underrepresented (Ågren et al., 2015; Brooks and Colburn, 2011; Fritz et al., 2013). Inadequate representation of the stream network can significantly impact the modeled retention capacity of riparian buffer strips (Baker et al., 2007) and thus solute export.

Travel time, i.e., the time it takes a raindrop to reach the catchment outlet, is an important control on the transport and fate of nutrients and contaminants as well as mineral weathering. Because stream network expansion shortens the distances between hillslopes and flowing streams, it must also affect the distribution of travel times. However, most studies interpret temporal variations in travel time distributions in terms of the relative contributions of fast and slow flow pathways and changes in the residence times of different storage zones, ignoring the effects of changes in the flowing stream network on subsurface flowpath lengths (Benettin et al., 2015a; Harman, 2014; van der Velde et al., 2012; Yang et al., 2018). Young water fractions were correlated with the drainage densities across 22 Swiss catchments, suggesting that denser drainage networks, and thus shorter subsurface flow paths, promote faster transport of recent precipitation (von Freyberg et al., 2018a). Hydrological modeling has similarly suggested a larger contribution of young water for lowland catchments with higher drainage densities and thus presumably shorter travel distances (Kaandorp et al., 2018).

Here, using simple graphical analyses of field-mapped stream networks, we show that network extension and retraction not only change subsurface travel distances and thus catchment-scale travel times, but also change the shape of the travel time distribution. Our results imply that changes in the flowing stream network should be taken into account when modeling catchment-scale solute transport or interpreting travel time distributions.

Extension of the flowing stream network during wet conditions significantly shortens the subsurface flow pathways (shown in red for five selected locations A–E in Fig. 3). This not only shortens the average and median travel time to the outlet, but also changes the shape of the travel time distribution (Table 2 and Fig. 4a–d). For the extended flowing stream networks typical of wet conditions, most subsurface travel distances (and thus travel times) are short, but for the retracted networks typical of dry conditions, the travel times are longer and more uniformly distributed. When the flowing stream network is greatly retracted during extremely dry periods, almost the entire catchment has travel times longer than 2 d and thus could not contribute to storm flow in response to a brief rainfall event. However, when the flowing stream network is fully extended, most of the catchment could contribute to storm flow at the outlet because the travel times are mainly short (Fig. 4d). The correspondence between flowing stream networks and travel time distributions is not one to one, however. For example, even though the flowing stream network during the dry conditions in November 2016 is different from the network shown on the topographic map (Fig. 2b and e), the cumulative frequency distributions of the travel times are similar (Fig. 5).

The travel time distribution for the stream network during the wetting-up period (October 2016 mapping) is bimodal (Fig. 4c) due to the large area with flowing streams that is disconnected from the outlet by the dry stream section in the steeper part of the catchment (Table 1 and Fig. 2c). For the selected subsurface velocity (vh) of 5×10-4 m s-1, almost 2 d are required to cross the dry part of the channel as subsurface flow. A less apparent bi-modal travel time distribution also results from disconnection of the flowing stream network during the extremely dry conditions of August 2018 (Fig. 4a).

The chosen surface and subsurface velocities do not substantially affect the shapes of the travel time distributions (Fig. 6). Changing the assumed subsurface velocity (and thus the ratio of the surface to subsurface velocities) by large factors has the effect of rescaling the travel time distributions, but does not substantially change their shapes (Fig. 6). This is to be expected. The shapes of the travel time distributions will be mainly determined by the distribution of subsurface travel distances (Lh), whenever velocities are assumed to be constant in space and time and slower in the subsurface than the surface. Under these assumptions, the subsurface travel times (th) will be much longer than the surface flow travel times (ts), and thus will largely determine the travel time distribution. Reasonable ranges of assumed surface flow velocities have virtually no effect on the travel time distributions, due to the very small contribution of the surface flow travel times (ts) to the total travel times (tt).

By only changing the flowing stream network and keeping all other variables (such as the velocities) constant, our analysis shows how the extension and retraction of the flowing stream network affect subsurface flowpath lengths and catchment-scale travel times. In practice, the effects of catchment wetness on travel time distributions will be larger than shown here, because subsurface flow velocities will be smaller during dry conditions, significantly increasing travel times when the stream network is most contracted. Subsurface flow velocities will also vary spatially, which will further broaden the travel time distributions. Furthermore, subsurface flow directions may not follow the surface topography and may change depending on water table gradients and thus wetness conditions (Rodhe and Seibert, 2011; van Meerveld et al., 2015), and some areas of the catchment may not contribute to streamflow during dry conditions (Jencso et al., 2010; Zuecco et al., 2019). By excluding these confounding factors, we could isolate the effect of stream network geometry on travel times and show that stream network extension and retraction significantly alter the mean and median travel times as well as the shape of the travel time distribution.

Previous modeling studies have suggested that streamflow consists of a larger fraction of young water during wet conditions than during dry conditions. For example, Benettin et al. (2015b) calibrated a hydrological model for the Plynlimon catchment in Wales using both streamflow and stream chloride data and suggested that the travel time distribution was much more skewed towards younger water during wet conditions. Visser et al. (2019) used a combination of isotope tracers to constrain a hydrological model for a Sierra Nevada catchment and inferred that the travel time distribution was skewed towards younger water during high-flow conditions but was nearly uniform during baseflow (although this was partly due to a lack of young water in storage due to drought conditions). This change in the streamflow travel time distribution (and the storage selection function) with catchment wetness conditions is generally attributed to a larger contribution from shallower and faster flow pathways during wetter conditions (Benettin et al., 2015b; Harman, 2014; Hrachowitz et al., 2016; van der Velde et al., 2012). Although the travel times in these studies were much longer than we calculated here, in part because we assumed that surface and subsurface flow velocities would not decrease during dry conditions, our results suggest that the dynamics of the flowing stream network alone can lead to significant changes in travel time distributions. Therefore, these network dynamics and the associated changes in subsurface travel distances need to be taken into account when interpreting time-varying travel time distributions. Above all, more studies are needed where detailed tracer sampling is combined with detailed stream network mapping to determine how stream network extension affects travel time distributions. Our results also suggest the speculative possibility that the dynamics of stream network extension and retraction could potentially be inferred from the time-varying behavior of travel time distributions.

Our results, furthermore, suggest that stream networks shown on the topographic maps may loosely approximate the flowing stream network during dry conditions, but not during wet conditions. When these static networks are used for modeling studies, the modeled flow pathways may be far longer than the real-world subsurface flow paths, particularly during wet conditions (see also Zimmer and McGlynn, 2018). The resulting modeled transit time distributions would then be much less skewed than those in the real world. This would lead to much slower modeled transport of pollutants, unless compensated otherwise (e.g., via unrealistically high velocities or large areas with surface runoff, as for example shown for flow on the Greenland ice sheet by Yang et al., 2018). Therefore, solute transport studies need to take the complexities of stream network extension and retraction into account, particularly in locations where (or at times when) the network may be very dynamic. This will require better knowledge of the processes and catchment characteristics that control flowing stream network extension and retraction, since it is impractical to map the dynamics of the flowing stream network in every catchment. As more field maps of network extension and retraction become available, empirical generalizations about stream network dynamics and their controlling factors will become more reliable. As an example of what may be possible, Prancevic and Kirchner (2019) have recently shown that topography may be a useful predictor of where the flowing stream network is highly dynamic and where it is more stable. Using either empirical generalizations from the limited available field studies, predictive relationships like those suggested by Prancevic and Kirchner (2019), or modeled stream networks (Russell et al., 2015; Ward et al., 2018; Williamson et al., 2015) would be better than assuming that flowing stream networks are static.

We estimated travel time distributions for different mapped stream networks by calculating the subsurface transport distance from each pixel to the nearest flowing stream and the surface transport distance along the stream network to the outlet for different flowing stream networks. Our results show that extension and retraction of flowing stream networks can significantly alter catchment travel time distributions, even if all other factors remain constant. When stream networks extend during wet conditions, travel times become shorter and their distributions become more skewed. Conversely, when stream networks retract during dry conditions, travel times become longer and more uniformly distributed. The effects of flowing stream network dynamics will be even more significant in the real world than calculated here, because we assumed that velocities did not change with wetness conditions, in order to isolate the effect of stream network geometry alone. Our simple graphical analysis implies that the dynamics of the flowing stream network need to be taken into account when interpreting travel time distributions or modeling solute transport. This will require better documentation of stream network extension and retraction in more diverse landscapes and climatic conditions, coupled with a better understanding of the processes and catchment characteristics that control flowing stream network dynamics.