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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. 

Systematic variations in atmospheric heat exchange, surface residence time, and groundwater influx across montane stream networks commonly produce an increasing stream temperature trend with decreasing elevation. However, complex stream temperature profiles that differ from this common longitudinal trend also exist, suggesting that stream temperatures may be influenced by complex interactions among hydrologic and atmospheric processes. Lakes within stream networks form one potential source of temperature profile complexity due to the spatially variable contribution of lake‐sourced water to stream flow. We investigated temperature profile complexity in a multi‐season stream temperature dataset collected across a montane stream network containing many alpine lakes. This investigation was performed by making comparisons between multiple statistical models that used different combinations of stream and lake characteristics to represent specific hypotheses for the controls on stream temperature. The compared models included a set of models which used a topographically derived estimate of the hydrologic influence of lakes to separate and quantify the effects of stream elevation and lake source‐water contributions to longitudinal stream temperature patterns. This source‐water mixing model provided a parsimonious explanation for complex stream‐network temperature patterns in the summer and autumn, and this approach may be further applicable to other systems where stream temperatures are influenced by multiple water sources. Simpler models that discounted lake effects were more optimal during the winter and spring, suggesting that complex patterns in stream temperature profiles may emerge and subside temporally, across seasons, in response to diversity of water temperatures from different sources.