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.

Direct-runoff and baseflow are the two primary components of total streamflow and their accurate estimation is indispensable for a variety of hydrologic applications. While direct runoff is the quick response stemming from surface and shallow subsurface flow paths, and is often associated with floods, baseflow represents the groundwater contribution to streams and is crucial for environmental flow regulations, groundwater recharge, and water supply, among others. L’vovich (1979) proposed a two-step water balance where precipitation is divided into direct runoff and catchment wetting followed by the disaggregation of the latter into baseflow and evapotranspiration. Although arguably a better approach than the traditional Budyko framework, the physical controls of direct runoff and baseflow are still not fully understood. Here, we investigate the role of the aridity index (ratio between mean annual potential evapotranspiration and precipitation) in controlling the long-term (mean-annual) fluxes of direct runoff and baseflow. We present an analytical solution beginning with similar assumptions as proposed by Budyko (1974), leading to two complementary expressions for the two fluxes. The aridity index explained 83% and 91% of variability in direct runoff and baseflow from 499 catchments within the continental US, and our formulations were able to reproduce the patterns of water balance proposed by L’vovich (1979) at the mean annual timescale. Our approach allows for the prediction of baseflow and direct runoff at ungauged basins and can be used to further understand how climate and landscape controls the terrestrial water balance at mean annual timescales.

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.

The calibration of global hydrological models has been attempted for over two decades, but an effective and generic calibration method has not been proposed. In this study, we investigated the application of Approximate Bayesian Computation (ABC) to calibrate the H08 global hydrological model by running global simulations with 5000 randomly generated sets of four sensitive parameters. This yielded satisfactory results for 777 gauged watersheds, indicating that ABC can be used to optimize H08 parameters to calibrate individual watersheds. We tested the identifiability of the parameters to yield satisfactory representations of hydrological functions based on Köppen’s climate classification (“climate-based” calibrations hereafter) We aggregated 5000 simulation results per catchment based on the 11 Köppen climate classes, then selected the parameters that exceeded the Nash–Sutcliffe efficiency (NSE) scores predefined by the acceptance ratio for each climate class. Our results indicate that the number of stations showing satisfactory (NSE > 0.0) and good (NSE>0.5) performances were 480 and 234 (61.7% and 30.1% of total stations, respectively), demonstrating the effectiveness of climate-based calibration. We also showed that the climate-based parameters outperformed the default and global parameters in terms of representativeness (global-scale differences of hydrological properties among climate classes) and robustness (consistency in yielding satisfactory results for watersheds in the same climate class). The identified parameters for 11 Köppen climate classes showed consistency with the physical interpretation of soil formation and efficiencies in vapor transfer with a wide variety of vegetation types, corroborating the strong influence of climate on hydrological properties.

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.