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  1. Abstract

    Flow recession analysis, relating dischargeQand 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/dtversusQ, 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 ensemble characteristics 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. We examine if those approaches can be reconciled. We utilize a machine learning tool to capture the point cloud using the past trajectory of daily discharge. Our model results for a catchment 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.

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  2. Abstract

    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 the 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 mapping of 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 neighboring 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 the Richards equation, which requires the heterogeneous field of material properties, at the hillslope scale and shows the relevance to improving our understanding of effective parameters to be able to apply the process‐based model to larger scales.

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  3. Abstract

    Spatially integrated transport models have been applied widely to model hydrologic transport. However, we lack simple and process‐based theoretical tools to predict the transport closures—transit time distributions (TTDs) and StorAge Selection (SAS) functions. This limits our ability to infer characteristics of hydrologic systems from tracer observations and to make first‐order estimates of SAS functions in catchments where no tracer data is available. Here we present a theoretical framework linking TTDs and SAS functions to hydraulic groundwater theory at the hillslope scale. For hillslopes where the saturated hydraulic conductivity declines exponentially with depth, analytical solutions for the closures are derived that can be used as hypotheses to test against data. In the simplest form, the hillslope SAS function resembles a uniform or exponential distribution (corresponding to flow pathways in the saturated zone) offset from zero by the storage in the unsaturated zone that does not contribute to discharge. The framework is validated against nine idealized virtual hillslopes constructed using a 2‐D Richards equation‐based model, and against data from tracer experiments in two artificial hillslopes. Modeled internal age, life expectancy, and transit time structures reproduce theoretical predictions. The experimental data also support the theory, though further work is needed to account for the effects of time‐variability. The shape and tailing of TTDs and their power spectra are discussed. The theoretical framework yields several dimensionless numbers that can be used to classify hillslope scale flow and transport dynamics and suggests distinct water age structures for high or low Hillslope number.

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  4. Abstract

    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. In this study, we estimated time‐variable TTD of a bench‐scale bare‐soil sloping soil lysimeter through the StorAge Selection (SAS) framework, a traditional lumped‐systems method, based on sampling of output tracer concentrations, as well as through an ERI SAS one, 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.

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