The Sensitivity of Hyporheic Exchange to Fractal Properties of Riverbeds

Abstract

Hyporheic exchange in riverbeds is driven by current-bed topography interactions. Because riverbeds exhibit topographic roughness across scales, from individual grains to bedforms and bars, they can exhibit fractal patterns. This study analyzed the influence of fractal properties of riverbed topography on hyporheic exchange. A set of synthetic fractal riverbeds with different scaling statistics was used as inputs to sequentially coupled numerical simulations of turbulent channel flow and hyporheic flow. In the analysis, the maximum power spectrum (dune size) and the fractal dimension (topographic complexity) were considered as independent variables and we then investigated how interfacial fluxes and hyporheic travel times are functionally related to these variables. As the maximum power spectrum increases (i.e., dune height to flow depth ratio), the average interfacial flux increases logarithmically whereas it increases exponentially with an increase in fractal dimension. Hyporheic exchange is more sensitive to additional roughness (larger fractal dimensions) than to bedform size (larger maximum power). Our results imply that fractal properties of riverbeds are crucial to predicting hyporheic exchange. The predictive relationships we propose could be integrated with reduced complexity, large-scale models. They can also be used to design artificial topographies that target hyporheic ecosystem services.

The Role of Hyporheic Connectivity in Determining Nitrogen Availability: Insights From an Intermittent Antarctic Stream

“…Surprisingly, our data suggest that variations in streamflow did not result in a shift from transport‐to reaction‐limitation for remineralization and nitrification in the hyporheic zone as concentrations remained fairly stable. It is notable that, even in well‐studied perennial systems, there is conflicting evidence of how hyporheic exchange scales with discharge across geomorphologies (Lee et al., 2020; Ward et al., 2012; Wondzell, 2006; Wondzell & Gooseff, 2013; Zimmer & Lautz, 2014) and how N uptake rates are affected (Webster et al., 2003), although evidence from MDV streams suggests hyporheic turnover increases during periods of higher flow (Singley et al., 2017). While we cannot constrain actual rates on any particular process from the data, it is notable that cycling of autochthonous N in the hyporheic zone of Von Guerard Stream must occur on timescales sufficiently fast to counteract transport losses, or shifts in residence time, that can occur due to successive flow pulses (Singh et al., 2020).…”

Hyporheic hydraulic geometry: Conceptualizing relationships among hyporheic exchange, storage, and water age

“…Consider, for instance, the fact that power-law scaling may break down for very low water ages [54]. Such a result might be expected, given the fractal nature of nested hyporheic flow paths [55]. Just as the measured length of any coastline is dependent upon the scale of measurement, the magnitude of any empirical or modeled estimate of q # must be dependent upon some inherent minimum time-scale of water age.…”

Surface Transient Storage Under Low‐Flow Conditions in Streams With Rough Bathymetry

“…(2015) related the residence‐time distribution to the fractality of the rough‐bed topography obtained from laser scanning at a very high resolution, followed by Lee et al. (2020) in a numerical work exploring the dependence of both interfacial fluxes and hyporheic travel times on the fractal properties. Some studies have explored the surface transient storage caused by structured cavities or groynes (McCoy et al., 2008; Jackson, Haggerty, Apte, & O’Connor, 2013, 2015).…”

“…Femeena et al (2019) performed a meta-analysis of previous tracer studies proposing concise laws to predict transient-storage parameters to river characteristics. Through laboratory-scale experiments and numerical simulations, Aubeneau et al (2015) related the residence-time distribution to the fractality of the rough-bed topography obtained from laser scanning at a very high resolution, followed by Lee et al (2020) in a numerical work exploring the dependence of both interfacial fluxes and hyporheic travel times on the fractal properties. Some studies have explored the surface transient storage caused by structured cavities or groynes (McCoy et al, 2008;Jackson, Haggerty, Apte, & O'Connor, 2013.…”