Fractal patterns in riverbed morphology produce fractal scaling of water storage times

Abstract

River topography is famously fractal, and the fractality of the sediment bed surface can produce scaling in solute residence time distributions. Empirical evidence showing the relationship between fractal bed topography and scaling of hyporheic travel times is still lacking. We performed experiments to make high‐resolution observations of streambed topography and solute transport over naturally formed sand bedforms in a large laboratory flume. We analyzed the results using both numerical and theoretical models. We found that fractal properties of the bed topography do indeed affect solute residence time distributions. Overall, our experimental, numerical, and theoretical results provide evidence for a coupling between the sand‐bed topography and the anomalous transport scaling in rivers. Larger bedforms induced greater hyporheic exchange and faster pore water turnover relative to smaller bedforms, suggesting that the structure of legacy morphology may be more important to solute and contaminant transport in streams and rivers than previously recognized.

Channel Filtering Generates Multifractal Solute Signals

“…At reach scales these include hydrodynamic dispersion and exchange with hyporheic storage zones (Haggerty et al, ; Lindgren et al, ). Experimental studies (Aubeneau et al, ) have demonstrated how the fractal nature of streambed morphology results in exchange between the channel and hyporheic storage zones producing long‐tailed power law distributed TTDs (Gooseff et al, ; Haggerty et al, ), consistent with values of α SC observed here. Variation in the magnitude of hyporheic exchange in response to morphological structure of the channel (Gooseff et al, ) controls the TTD and potentially explains differences in fitted α SC values across catchments (though not across solutes within catchments).…”

“…Various models have been proposed (Kirchner et al, 2001;Kollet & Maxwell, 2008;Scher et al, 2002) to explain how dispersion and retention in the catchment subsurface during transport through the hillslope to the stream generate 1/f solute scaling behavior over a broad range of time scales. It has also been noted that in-channel storage and hyporheic exchange can generate 1/f scaling (Aubeneau et al, 2015;Haggerty et al, 2002), though only up to time scales on the order of hours to days, consistent with stream TTDs (Haggerty et al, 2002). However, superposition of these processes (i.e., stream channel filtering of~1/f signals delivered from hillslope), acting at different timescales, should presumably generate multifractal behavior (i.e., spectral slopes that cannot be characterized by a single exponent at all scales).…”

River corridor science: Hydrologic exchange and ecological consequences from bedforms to basins

“…At the basin scale, geologic factors such as valley slope and the extent and texture of the valley fill and alluvial sediments are important controls on hydrologic exchange flows [ Larkin and Sharp , ; Woessner , ]. The size and frequency of channel‐forming flows and texture of bed sediments determine the channel's geometry, including bankfull width, sinuosity, and types, sizes, and spacing of bedforms and barforms, all of which influence hydrologic exchange flows [ Aubeneau et al ., ; Martin and Jerolmack , ]. Hydrologic exchanges vary with time during spates and floods [ Ward et al ., ; Zimmer and Lautz , ] and punctuated discharge and water level variations in rivers regulated for hydropower also generate fluctuating surface‐subsurface exchange flows [ Sawyer et al ., ].…”

“…[], Kiel and Cardenas [], and Gomez‐Velez and Harvey []). As always, heterogeneity in the types and sizes of buried alluvium [ Heeren et al ., , ; Menichino et al ., ], and heterogeneity of barforms, grain sizes, and subsurface hydraulic conductivity [ Aubeneau et al ., ; Cardenas et al ., ], and interactions with other types of roughness features (bioroughness, e.g., aquatic vegetation and downed wood in rivers) [ Jackson et al ., ; Wohl et al ., ] are crucial in their effect on hydrologic exchange flows and fate of dissolved and suspended materials in rivers. Another challenge is developing practical tools of measuring hydrologic exchange fluxes that avoid the potential bias of using a single technique, since no matter what method is used, it has a limited range of sensitivity that may only detect a portion of the water and chemical fluxes crossing hydrologic interfaces [ Cook and Herczeg , ; Harvey and Wagner , ].…”

Surface water‐groundwater connectivity in deltaic distributary channel networks

“…These deeper storage zones may contribute trace contaminant loads to surface waters over long periods. Solute storage in catchments is also fractal [ Haggerty et al, ; Kirchner et al, ], due in part to the self‐similarity of groundwater flow patterns beneath self‐similar topographic features [ Aubeneau et al, ; Cardenas , ]. The topographic features in deltas that drive groundwater flow range across scales from ripples within distributary channels to whole islands.…”