Understanding transit times (TT) and residence times (RT) distributions of water in catchments has recently received a great deal of attention in hydrologic research since it can inform about important processes relevant to the quality of water delivered by streams and landscape resilience to anthropogenic inputs. The theory of transit time distributions (TTD) is a practical framework for understanding TT of water in natural landscapes but, due to its lumped nature, it can only hint at the possible internal processes taking place in the subsurface. While allowing for the direct observation of water movement, Electrical Resistivity Imaging (ERI) can be leveraged to better understand the internal variability of water ages within the subsurface, thus enabling the investigation of the physical processes controlling the time-variability of TTD. We estimated time variable TTD through the storage selection (SAS) framework following a traditional lumped-systems approach, based on sampling of output tracer concentrations, as well as through an ERI SAS approach based on spatially distributed images of water ages. We compared the ERI-based SAS results with the output-based estimates to discuss the viability of ERI at laboratory experiments for understanding TTD. The ERI-derived images of the internal evolution of water ages were able to elucidate the internal mechanisms driving the time-variability of ages of water being discharged by the system, which was characterized by a delayed discharge of younger water starting at the highest storage level and continuing throughout the water table recession.

The direct observation of water movement via Electrical Resistivity Imaging (ERI) can leverage the understanding of the processes that lead to the occurrence of variable residence times (RT) within the Critical Zone (CZ). While hydrological processes at natural landscapes are often space and time-variable, quantitatively estimating solute transport with ERI under transient conditions is challenging due to necessary considerations of moisture states and electrical properties of the medium. Here, we introduce the use of Periodic Steady State (PSS) theory applied to electrical resistivity of soils to provide a simple solution to the problems and report a laboratory experiment to test the proposed method. We used a 1 m3 sloping lysimeter to represent the hydrological functioning of natural hillslopes, equipped with electrodes to provide cross-borehole images of bulk soil electrical conductivity and performed a 28-days experiment in which a periodic irrigation was applied. A saline tracer was added to the lysimeter in two irrigation pulses and subsequent pulses were applied until the tracer was flushed out. ERT-surveys and estimates of background soil-water conductivity were used to quantitatively estimate solute breakthrough throughout the different cross-sections. Integrated lysimeter-scale images were superimposed with the water table progression throughout the experiment to leverage the understanding of flow and transport processes responsible for the tracer mobilization. Our study introduces a novel method for laboratory experimentation at mesocosm scales using ERT and provides valuable insight into the role of water table dynamics in mediating the occurrence of variable flow pathways within hillslopes.

Flow recession analysis, relating discharge Q and its time rate of change -dQ/dt, has been widely used to understand catchment scale flow dynamics. However, data points in the plot of -dQ/dt versus Q typically form a wide point cloud due to noise and hysteresis, and it is still unclear what information we can extract from the data points and how to understand the information. In this study, we utilize a machine learning tool to capture the point cloud using the past trajectory of discharge. Our results show that most of the data points can be captured using 5 days of past discharge. While analyzing the machine learning model structure and the trained parameters is a daunting task, we show that we can learn the catchment scale flow recession dynamics from what the machine learned. We analyze patterns learned by the machine and explain and hypothesize why the machine learned those characteristics. The hysteresis in the plot mainly occurs during the early time dynamics, and the flow recession dynamics eventually converge to an attractor in the plot, which represents the master recession curve. We also illustrate that a hysteretic storage-discharge relationship can be estimated based on the attractor.

Flow recession analysis, relating discharge Q and its time rate of change -dQ/dt, has been widely used to understand catchment scale flow dynamics. However, data points in the recession plot, the plot of -dQ/dt versus Q, typically form a wide point cloud due to noise and hysteresis in the storage-discharge relationship, and it is still unclear what information we can extract from the plot and how to understand the information. There seem to be two contrasting approaches to interpret the plot. One emphasizes the importance of the ensembles of many recessions (i.e., the lower envelope or a measure of central tendency), and the other highlights the importance of the event scale analysis and questions the meaning of the ensemble characteristics. In this study, we examine if those approaches can be reconciled. We utilize a machine learning tool to capture the point cloud using the past trajectory of discharge. Our results show that most of the data points can be captured using 5 days of past discharge. We show that we can learn the catchment scale flow recession dynamics from what the machine learned. We analyze patterns learned by the machine and explain and hypothesize why the machine learned those characteristics. The hysteresis in the plot mainly occurs during the early time dynamics, and the flow recession dynamics eventually converge to an attractor in the plot, which represents the master recession curve. We also illustrate that a hysteretic storage-discharge relationship can be estimated based on the attractor.

Spatially-integrated water transport dynamics at the hillslope scale have rarely been observed directly, and underlying physical mechanisms of those dynamics are poorly understood. We present time-variable transit time distributions (TTDs) and StorAge Selection (SAS) functions observed during a 28 days tracer experiment conducted at the Landscape Evolution Observatory (LEO), Biosphere 2, University of Arizona, AZ, USA. The observed form of the SAS functions is concave, meaning that older water in the hillslope was discharged more than younger water. The concavity is, in part, explained by the relative importance of advective and diffusive water dynamics and by the geomorphologic structure of the hillslopes. A simple numerical examination illustrates that, for straight plan shape hillslopes, the saturated zone SAS function is concave when hillslope Peclet (Pe) number is large. We also investigated the effect of hillslope planform geometry on the SAS function: The more convergent the plan shape is, the more concave the SAS function is. A numerical examination also indicates that the unsaturated zone SAS function is concave for straight and convergent hillslopes, when the soil thickness is constant. The concavity of those sub-component SAS functions signifies that the hillslope scale SAS function is concave for straight or convergent plan shape hillslopes when the hillslope Pe number is high.

Process-based modeling of soil water movement with the Richards equation requires the description of soil hydraulic material properties, which are highly uncertain and heterogeneous at all scales. This limits the applicability of Richards equation at larger scales beyond the patch scale. The experimental capabilities of the three hillslopes of the Landscape Evolution Observatory (LEO) at Biosphere 2 provide a unique opportunity to observe the heterogeneity of hydraulic material properties at the hillslope scale. We performed a gravity flow experiment where through constant irrigation the water content increases until the hydraulic conductivity matches the irrigation flux above. The dense water content sensor network at LEO then allows to map the heterogeneity of hydraulic conductivity at a meter scale resolution. The experiment revealed spatial structures within the hillslopes, mainly a vertical trend with the lowest hydraulic conductivity close to the surface. However, the variation between neighbouring sensors is high, showing that the heterogeneity cannot be fully resolved even at LEO. By representing the heterogeneity in models through Miller scaling we showed the impact on hillslope discharge. For the hillslope with the smallest heterogeneity, representing the dominant structures was sufficient. However, for the two hillslopes with the larger overall heterogeneity, adding further details of the local heterogeneity did impact the discharge further. This highlights the limitations of Richards equation, which requires the heterogeneous field of material properties, at the hillslope scale and shows the relevance to improve our understanding of effective parameters to be able to apply the process-based model to larger scales.

Uncovering the hillslope scale flow and transport dynamics in an experimental hydrologic systemMinseok Kim1, Till H. M. Volkmann1,2, Aaron Bugaj1, Yadi Wang3, Antônio A. Meira Neto4, Katarena Matos4, Ciaran J. Harman5,6, Peter A. Troch1,41Biosphere 2, University of Arizona, Tucson, AZ, USA,2Applied Intelligence, Accenture, Kronberg im Taunus, Germany, 3Department of Environmental Science, University of Arizona, Tucson, AZ, USA, 4Department of Hydrology and Atmospheric Sciences, University of Arizona, Tucson, AZ, USA, 5Department of Environmental Health and Engineering, Johns Hopkins University, Baltimore, MD, USA,6Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD, USAHillslope scale water flow and transport dynamics have been extensively studied (Burt & McDonnell, 2015; Hewlett & Hibbert, 1963), but observing those internal dynamics in high spatial and temporal resolutions remains challenging. In this study, we uncover internal water flow and transport dynamics in an artificial hillslope in the Landscape Evolution Observatory (LEO), Biosphere 2, University of Arizona, Tucson, USA, using the experimental dataset collected in December 2016. Complete information about the hillslope and experiment can be found elsewhere (Pangle et al., 2015; Till H. M. Volkmann et al., 2018); Here, we only summarize some relevant information.The first part of the animation describes the experimental system and setup (time 00:12 – 04:14 in Animation S1). The LEO hillslope is 330 m3 (30 m long, 11 m wide, and 1 m deep) sloping soil lysimeter. The hillslope is primarily made up of loamy-sand textured basaltic tephra, and the most downslope 5.5 m3 is filled with gravel-textured basaltic tephra. A custom irrigation system supplies reverse osmosis filtered water onto the LEO surface. The downslope boundary is exposed to atmospheric pressure, creating the seepage face boundary condition. The sensor networks (including pressure transducers and volumetric water content sensors) and the water isotope sampling locations and intervals (7 hrs to 101 hrs) are illustrated in Animation S1 (time 02:09 – 03:01). The isotope composition of subsurface water is obtained from laser-based online measurements of vapor that is extracted via custom gas probes through equilibrium calculation (T. H.M. Volkmann & Weiler, 2014). The irrigation sequence of this experiment was designed to generate a periodic steady state, which allows the application of the PERidoic Tracer Hierarchy method (Harman & Kim, 2014) for the observation of the time-variable transit time distributions and the StorAge Selection functions. Deuterium-labeled water was irrigated during the first two irrigation events.The second part of the animation shows the dynamics of the perched water table and soil water content (time 04:15 – 06:53). The extent of the saturated zone was estimated using the pressure transducer data and Delaunay triangulation (Delaunay, 1934). The experimental data show the saturation from below mechanisms—wetting up from the bedrock surface into the soil profile (McDonnell, 1997)—and the saturation from downslope to upslope. The water table profile forms a wedge-like shape, which is a characteristic of hillslope with a high hillslope (Peclet) number (Berne et al., 2005; Brutsaert, 1994). The hillslope Peclet number of the LEO hillslope during the experiment is high (> 10) (Kim et al., 2020). Significant time delays in the water table dynamics are observed at some upslope locations (e.g., at 13 m upslope), which is mostly due to the delayed water supply from the convergent upslope area. The water content data indicates that the convergent upslope water content began to decrease around the timing of the water table peak at 13 m upslope.The third part of the animation shows the tracer dynamics (from time 06:43). The animated experimental data reveal two notable water transport dynamics. First, the vertical tracer movement is faster at the upslope. This faster movement at the upslope is, in a sense, counter-intuitive because the upslope region is drier than the downslope. This is due to the lateral flow in the saturated zone and the tension saturated zone, that are thicker at the downslope. While water velocity is higher at the downslope, the direction of velocity is not vertical but rotated towards the downslope in those zones.Second, the animated data illustrate that old water is present only at the downslope. This observation is a characteristic of hillslope with a high hillslope number, in which old water is preferentially discharged (Kim et al., 2020). Indeed, the observed SAS function in this hillslope is concave (Kim et al., 2020), indicating that the hillslope preferentially discharges old water that is stored at the downslope.