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.

Abstract:In this study, an artificial neural network (ANN) model is developed to predict the stability number of breakwater armor stones based on the experimental data reported by Van der Meer in 1988. The harmony search (HS) algorithm is used to determine the near-global optimal initial weights in the training of the model. The stratified sampling is used to sample the training data. A total of 25 HS-ANN hybrid models are tested with different combinations of HS algorithm parameters. The HS-ANN models are compared with the conventional ANN model, which uses a Monte Carlo simulation to determine the initial weights. Each model is run 50 times and the statistical analyses are conducted for the model results. The present models using stratified sampling are shown to be more accurate than those of previous studies. The statistical analyses for the model results show that the HS-ANN model with proper values of HS algorithm parameters can give much better and more stable prediction than the conventional ANN model.

Gradients in total head along a sediment-water interface (SWI) force water in and out of the porous and permeable sediment, defining a region flushed by river water known as the hyporheic zone. In flowing environments, the total head consists of hydrostatic and nonhydrostatic (i.e., hydrodynamic) components. The hydrostatic components are the elevation head and the hydrostatic pressure head. In open channels, this piezometric head is the water surface, the hydrostatic pressure head is the flow depth, and the hydrostatic gradient is the water surface slope (Thibodeaux & Boyle, 1987). The hydrodynamic head is due to the mean flow velocity-head (U 2 /2g where U is the flow velocity and g is the gravitational acceleration) and other nonhydrostatic forces related to the velocity and its distribution such as friction losses, turbulent stresses, and local accelerations (Chow, 1959). The balance between the dynamic and static components of pressure in the mean flow is concisely captured in the Froude number, which is a dimensionless ratio of (average) flow velocity (U) and water depth (d m),  U / m Fr gd. Thus, the Froude number is likely an important parameter for hyporheic zone processes. Streambed topography affects the local balance between the static and the dynamic forces that control bedform-driven hyporheic exchange. Assuming a flat water surface (i.e., a rigid-lid), the flow is constricted at the apex of a bedform where continuity requires that it is faster and energy conservation requires that the static head be lower (ignoring losses). These pressure changes drive an advective pumping flow through the porous sediment down the pressure gradients from the locations of high pressures to places of low pressures via a Venturi effect (Cardenas & Wilson, 2007a; Elliott & Brooks, 1997; Harvey et al., 2012; Marion et al., 2002). In real streams, the water surface is free to move and can adjust to the topography. When a free-surface flow goes over a step or a bedform, the hydrostatic pressure-drop incurred corresponds to a decrease in flow depth. If the flow becomes critical, nonlinear adjustments such as choking and hydraulic jumps can be observed (Chin, 2016). The differences between the pressure profiles (and the associated hyporheic fluxes) in idealized rigid-lid and in more realistic free-surface models have not been explored. Often considered models of hyporheic

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