On the propagation of diel signals in river networks using analytic solutions of flow equations

Abstract

Abstract. Several authors have reported diel oscillations in streamflow records and have hypothesized that these oscillations are linked to evapotranspiration cycles in the watershed. The timing of oscillations in rivers, however, lags behind those of temperature and evapotranspiration in hillslopes. Two hypotheses have been put forth to explain the magnitude and timing of diel streamflow oscillations during low-flow conditions. The first suggests that delays between the peaks and troughs of streamflow and daily evapotranspiration are due to processes occurring in the soil as water moves toward the channels in the river network. The second posits that they are due to the propagation of the signal through the channels as water makes its way to the outlet of the basin. In this paper, we design and implement a theoretical model to test these hypotheses. We impose a baseflow signal entering the river network and use a linear transport equation to represent flow along the network. We develop analytic streamflow solutions for the case of uniform velocities in space over all river links. We then use our analytic solution to simulate streamflows along a self-similar river network for different flow velocities. Our results show that the amplitude and time delay of the streamflow solution are heavily influenced by transport in the river network. Moreover, our equations show that the geomorphology and topology of the river network play important roles in determining how amplitude and signal delay are reflected in streamflow signals. Finally, we have tested our theoretical formulation in the Dry Creek Experimental Watershed, where oscillations are clearly observed in streamflow records. We find that our solution produces streamflow values and fluctuations that are similar to those observed in the summer of 2011.

Separation of Scales in Transpiration Effects on Low Flows: A Spatial Analysis in the Hydrological Open Air Laboratory

“…These mechanisms cause an increase in the lag times from 3 to 11 hr for MW catchment outlet. This interpretation is consistent with the findings of Bond et al (), Fonley et al (), Moore et al (), and Wondzell et al (, ).…”

“…This dynamic was explained by the weakening of the coupling between the vegetation and stream during summer as the groundwater levels dropped. The time lags between transpiration and streamflow also varies seasonally due to changes in the flow paths (Barnard et al, 2010;Cadol et al, 2012;Deutscher et al, 2016;Fonley et al, 2016;Graham et al, 2013;Gribovszki et al, 2008;Kirchner, 2009;Szeftel, 2010;Szilágyi et al, 2008;Wondzell et al, 2007Wondzell et al, , 2010Yue et al, 2016).…”

The pulse of a montane ecosystem: coupled daily cycles in solar flux, snowmelt, transpiration, groundwater, and streamflow at Sagehen and Independence Creeks, Sierra Nevada, USA

“…3, 4, and 6, and in many previous studies, is the time lag between the daily cycles of solar flux and groundwater and streamwater levels: the solar flux peaks near noon, but the water levels reach their maximum (or, during ET-dominated periods, their minimum) in late afternoon or early evening. This time lag has been widely interpreted 380 as indicating the time it takes for a pulse of water from snowmelt (or, conversely, a pulse of water removal by ET) to reach the channel, or to travel downstream to the measurement point (e.g., Wicht, 1941;Jordan, 1983;Bond et al, 2002;Wondzell et al, 2007;Barnard et al, 2010;Graham et al, 2013;Fonley et al, 2016). Here we show that this is not primarily a travel-time lag, but rather a dynamical phase lag.…”

“…The timing of daily streamflow maxima and minima, and their lags relative to the daily peaks of snowmelt or ET rates, have also been widely interpreted as reflecting travel times and flow velocities through snowpacks, hillslopes, and river networks (e.g., Wicht, 1941;Jordan, 1983;Bond et al, 2002;Wondzell et al, 2007;Barnard et al, 2010;Graham et al, 2013;Fonley et al, 2016). These applications, like the missing streamflow method, invoke assumptions that are incompatible with those that underlie WTF approaches.…”

“…Figure 8a shows that these time lags remain several hours long for all aquifer time constants longer than about 0.1 day. These time lags, as well as the asymmetry of the discharge curves, have often been attributed to travel-time delays for transport through the snowpack, aquifer, or river network (Wicht, 1941;Jordan, 1983;Bond et al, 2002;Lundquist et al, 485 2005;Wondzell et al, 2007;Barnard et al, 2010;Graham et al, 2013;Fonley et al, 2016). Figure 7 shows instead that they can arise purely from the internal dynamics of the riparian aquifer itself, as it integrates either cyclic water inputs from snowmelt or cyclic riparian losses from ET.…”