Becky Fasth

Rapids are common in steep rivers, often forming where flow transitions from supercritical (Froude number, Fr > 1) to subcritical ( Fr < 1) through a hydraulic jump. When upstream Fr is supercritical but close to 1, this transition may occur as an undular hydraulic jump, exhibiting a train of stationary waves downstream of the jump toe. Previous studies proposed a method to estimate discharge using only UHJ wave spacing and channel width combined with a wave dispersion equation for large water depths relative to the UHJ wavelength. This method is based on the hypotheses that, by their presence, UHJs indicate near‐critical flow conditions ( Fr 1) and that wave celerity c is equal to and opposite the cross‐sectionally averaged flow velocity U . However, these hypotheses have not been thoroughly tested. We used data from published UHJ flume experiments to test the hypotheses that Fr 1 and c = U , compare the deep‐water and general wave dispersion equations, and evaluate the accuracy of discharge estimates. In these experiments, the stationary waves exhibited shallow depths relative to wavelength and flow was subcritical ( Fr < 1) when averaged across multiple wavelengths. Additionally, wave celerity more closely approximated the surface flow velocity than U . By using a Fr representative of actual conditions and applying a coefficient to correct for , the accuracy of the discharge estimates improved. This finding suggests that the critical flow‐based method is robust and can produce reliable streamflow estimates if the remotely observed wave trains are correctly interpreted as UHJs, without requiring in situ measurements.

We examined the relationship between winter snow accumulation and summer stream flow and temperature in the Pacific Northwest. Several papers have hypothesized that climate change will reduce snow accumulation, thereby reducing summer stream flows, and leading to higher stream temperatures, especially in the late summer. Long-term data from gaged watersheds located in the H. J. Andrews Experimental Forest allowed us to test this hypothesis. Over 20 years, maximum snowpacks have been highly variable, with annual maximum snowpacks ranging from 103 to 875 mm, but summers are typically dry and often rain free. Thus, snowmelt would appear to have a high potential to influence summer streamflow. Our analyses did not support the hypothesized relationships. While the size of snowpack explained variability in spring stream temperatures and streamflow, this relationship did not persist into the summer. Summer stream temperatures were poorly explained by spring precipitation and snowmelt metrics, and were, alternatively, best explained by streamflow, precipitation, and air temperature metrics across all watersheds and elevations. Our findings suggest for Mediterranean climates in the Pacific Northwest, snowpack variability has a limited relationship to summer stream temperatures and late summer streamflow. Instead, late-summer stream conditions appeared to be most influenced by multiple factors, including precipitation after snowmelt has ceased.

Critical flow theory provides a physical foundation for inferring discharge from measurements of wavelength and channel width made from images. In rivers with hydraulically steep local slopes greater than 0.01, flow velocities are high and the Froude number (ratio of inertial to gravitational forces) can approach 1.0 (critical flow) or greater. Under these conditions, undular hydraulic jumps (UHJ's) can form as standing wave trains at slope transitions or constrictions. The presence of UHJ's indicates that mean , implying that the velocity and depth of the flow and the spacing of the waves are uniquely related to one another. Discharges estimated from 82 Google Earth images agreed closely with discharges recorded at gaging stations ( = 0.98), with a mean bias of 1% 11%. This approach could provide reliable discharge information in many fluvial environments where critical flow occurs, which tend to be underrepresented in gage networks.

Volcanic provinces are among the most active but least well understood landscapes on Earth. Here, we show that the central Cascade arc, USA, exhibits systematic spatial covariation of topography and hydrology that are linked to aging volcanic bedrock, suggesting systematic controls on landscape evolution. At the Cascade crest, a locus of Quaternary volcanism, water circulates deeply through the upper ∼ 1 km of crust but transitions to shallow and dominantly horizontal flow as rocks age away from the arc front. We argue that this spatial pattern reflects a temporal state shift in the deep Critical Zone. Chemical weathering at depth, surface particulate deposition, and tectonic forcing drive landscapes away from an initial state with minimal topographic dissection, large vertical hydraulic conductivity, abundant lakes, and muted hydrographs toward a state of deep fluvial dissection, small vertical hydraulic conductivity, few lakes, and flashy hydrographs. This state shift has major implications for regional water resources. Drill hole temperature profiles imply at least 81 km 3 of active groundwater currently stored at the Cascade Range crest, with discharge variability a strong function of bedrock age. Deeply circulating groundwater also impacts volcanism, and Holocene High Cascades eruptions reflect explosive magma–water interactions that increase regional volcanic hazard potential. We propose that a Critical Zone state shift drives volcanic landscape evolution in wet climates and represents a framework for understanding interconnected solid earth dynamics and climate in these terrains.

Flowing lava and water have dramatically different physical properties but can form similar hydraulic structures, including undular hydraulic jumps, or standing wave trains. In water flows, undular hydraulic jumps are evidence of critical flow (Froude number ∼1) and open‐channel hydraulic theory provides a powerful tool for estimating flow depth and velocity. Monitoring these parameters in an active lava channel is inherently challenging, but essential for calculating lava discharge (effusion rate), a primary control on the rate of flow front advance and ultimate flow runout distance. We analyze undular hydraulic jumps in both water and lava flows to assess the conditions under which they form and, by extension, the potential use of critical flow theory to estimate, in real time, lava flow velocity, depth, and discharge. Experimental data for water flows show that these structures mark the transition from supercritical to subcritical flow. Undular hydraulic jumps in the near‐vent lava channel of the 2018 lower East Rift Zone eruption of Kīlauea, Hawaiʻi also reflect critical flow conditions; their wavelengths scale with flow depth and velocity, consistent with hydraulic theory. Calculated lava effusion rates are similar to estimates made using more traditional approaches (Jeffreys', 1925, https://doi.org/10.1080/14786442508634662, equation based on lava viscosity, density, and channel slope) and with lava volumes derived from topographic‐change mapping. From this we conclude that critical flow phenomena show great potential to track flow dynamics and inform hazard assessment for a wide range of geophysical fluids.

The methods for conducting reductionist ecological science are well known and widely used. In contrast, those used in the synthesis of ecological science (i.e., synthesis science) are still being developed, vary widely, and often lack the rigor of reductionist approaches. This is unfortunate because the synthesis of ecological parts into a greater whole is critical to understanding many of the environmental challenges faced by society. To help address this imbalance in approaches, we examine how the rigor of ecological synthesis science might be increased by using uncertainty as an evaluation metric—as a parallel to methods used in reductionist science. To estimate and understand uncertainty we propose that it be divided into four general classes: (1) measurement uncertainty (i.e., experimental error) as defined by precision and accuracy, (2) sampling uncertainty that reflects natural variation in space and time as quantified by classical statistical moments (e.g., mean and variance), (3) model prediction uncertainty which relates to the transformation of measurements into other variables of interest (e.g., plant dimensions to biomass), and (4) model selection uncertainty which relates to uncertainty about the form of the relationships used in models. Of these sources of uncertainty, model selection is the least understood and potentially, the most important, because it is integral to how components of a system are combined and it reflects imperfect knowledge about these relationships. To demonstrate uncertainty in synthesis science, we examine each source of uncertainty in an analysis that estimates the live tree biomass of a forest and how knowledge of each source can improve future estimates. By quantifying sources of uncertainty in synthesis science, it should be possible to make rigorous comparisons among results, to judge whether they differ within the bounds of measurement and knowledge, and to assess the degree to which scientific progress is being made. However, to be accepted as a standard method, best practices analogous to those used in reductionist science need to be developed and implemented.