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

Hyporheic exchange is now widely acknowledged as a key driver of ecosystem processes in many streams. Yet stream ecologists have been slow to adopt nuanced hydrologic frameworks developed and applied by engineers and hydrologists to describe the relationship between water storage, water age, and water balance in finite hydrosystems such as hyporheic zones. Here, in the context of hyporheic hydrology, we summarize a well-established mathematical framework useful for describing hyporheic hydrology, while also applying the framework heuristically to visualize the relationships between water age, rates of hyporheic exchange, and water volume within hyporheic zones. Building on this heuristic application, we discuss how improved accuracy in the conceptualization of hyporheic exchange can yield a deeper understanding of the role of the hyporheic zone in stream ecosystems. Although the equations presented here have been well-described for decades, our aim is to make the mathematical basis as accessible as possible and to encourage broader understanding among aquatic ecologists of the implications of tailed age distributions commonly observed in water discharged from and stored within hyporheic zones. Our quantitative description of “hyporheic hydraulic geometry,” associated visualizations, and discussion offer a nuanced and realistic understanding of hyporheic hydrology to aid in considering hyporheic exchange in the context of river and stream ecosystem science and management.

Impacts of Massive Sediment Input on the Channel Geometry Adjustment of Alluvial Rivers: Revisiting the North Fork Toutle River Case

In this study, the impacts of massive sediment input on channel geometry adjustment were analyzed across decades based on the downstream hydraulic geometry. Massive amounts of field data and evolution models showed that the alternation of degradation and aggradation in short-to-medium-term channel adjustment is common in evolving rivers. This phenomenon has always been challenging in research; most existing studies have focused on unidirectional adjustment in short-term channel adjustment. A few studies have considered the alternation of degradation and aggradation in short-to-medium-term channel adjustment, presuming that this phenomenon is caused by water and sediment changes. However, we found that the alternations also occurred under stable water and sediment transport in the North Fork Toutle River, southwestern Washington, USA. This adjustment across decades was analyzed by downstream hydraulic geometry in this study. It was concluded that the river consumes surplus energy to reach the optimal cross section through this short-to-medium-term adjustment under stable water and sediment transport. The objective of channel adjustment is minimal energy loss.

GEP- and MLR-based equations for stable channel analysis

For decades, research on stable channel hydraulic geometry was based on the following parameters: river discharge, dimensionless discharge, the median size of bed material and the slope. Although significant research has been conducted in this area, including applied machine learning to increase the geometry model prediction accuracy, there has been no remarkable improvement as the variables used to describe the geometry relationship remain the same. The novelty of this study is demonstrated by the parameters used in the stable channel geometry equations that outperform the existing equation's accuracy. In this research, sediment transport parameters are introduced and analysed by applying the multiple linear regression (MLR) and gene expression programming (GEP) methods. The new equation of the width, depth and bed slope can give much-improved results in efficiency and lower errors. Furthermore, a new parameter B/y is introduced in this study to solve the restriction issue, either in width or depth prediction. The results from MLR and GEP show that in addition to the existing hydraulic geometry parameter, the B/y parameter is also able to give high accuracy results for width and depth predictions. Both calibration and validation for the B/y parameter yield high R2 and NSE values with low mean squared errors and mean absolute errors.

Resistance Analysis of Morphologies in Headwater Mountain Streams

River flow velocity is determined by the energy available for flow motion and the energy fraction lost by flow resistance. We compared the performance of different equations for the Darcy-Weisbach resistance coefficient (f) and empirical equations to predict flow velocity. The set of equations was tested using data from the Quinuas headwater mountain river in the Andean region. The data was collected in three Cascades, two Step-pools, and one Plane-bed covering a wide range of velocity magnitudes. The results reveal that nondimensional hydraulic geometry equations (NDHG) with a Nash-Sutcliffe efficiency index (EF) varying from 0.6–0.85 provide the most accurate velocity prediction. Furthermore, the study proposes a methodology applicable to all morphologies for defining the NDHG parameters using easily measured field data. The results show an improvement in predictability with EF values in the range of 0.81–0.86. Moreover, the methodology was tested against data from the literature, which was not divided into morphologies providing EF values of around 0.9. The authors encourage the application of the presented methodology to other reaches to obtain additional data about the NDHG parameters. Our findings suggest that those parameters could be related to reach characteristics (e.g., certain characteristic grain size), and in that case, the methodology could be useful in ungauged streams.