ALBERT

Description: The advance of a chemical weathering front into the bedrock of a hillslope is often limited by the rate weathering products can be carried away, maintaining chemical disequilibrium. If the weathering front is within the saturated zone, groundwater flow downslope may affect the rate of transport and weathering – however, weathering also modifies the rock permeability and the subsurface potential gradient that drives lateral groundwater flow. This feedback may help explain why there tends to be neither ‘runaway weathering’ to great depth, nor exposed bedrock covering much of the earth, and may provide a mechanism for weathering front advance to keep pace with incision of adjacent streams into bedrock. This is the second of a two‐part paper exploring the co‐evolution of bedrock weathering and lateral flow in hillslopes using a simple low dimensional model based on hydraulic groundwater theory. Here we show how a simplified kinetic model of 1‐D rock weathering can be extended to consider lateral flow in a 2‐D hillslope. Exact and approximate analytical solutions for the location and thickness of weathering within the hillslope are obtained for a number of cases. A location for the weathering front can be found such that lateral flow is able to export weathering products at the rate required to keep pace with stream incision at steady state. Three pathways of solute export are identified: "diffusing up", where solutes diffuse up and away from the weathering front into the laterally flowing aquifer; "draining down", where solutes are advected primarily downward into the unweathered bedrock; and "draining along", where solutes travel laterally within the weathering zone. For each pathway, a different subsurface topography and overall relief of unweathered bedrock within the hillslope is needed to remove solutes at steady state. The relief each pathway requires depends on the rate of stream incision raised to a different power, such that at a given incision rate one pathway requires minimal relief, and therefore likely determines the steady‐state hillslope profile.

Description: Abstract A storage‐discharge relation tells us how discharge will change when new water enters a hydrologic system, but not which water is released. Does an incremental increase in discharge come from faster turnover of older water already in storage? Or are the recent inputs rapidly delivered to the outlet, ‘short‐circuiting’ the bulk of the system? Here I demonstrate that the concepts of storage‐discharge relationships and transit time distributions can be unified into a single relationship that can usefully address these questions: the age‐ranked storage‐discharge relation. This relationship captures how changes in total discharge arise from changes in the turn‐over rate of younger and older water in storage, and provides a window into both the celerity and velocity of water in a catchment. This leads naturally to a distinction between cases where an increase in total discharge is accompanied by an increase (old water acceleration), no change (old water steadiness), or a decrease in the rate of discharge of older water in storage (old water suppression). The simple theoretical case of a power‐law age‐ranked storage‐discharge relations is explored to illustrate these cases. Example applications to data suggest that the apparent presence of old water acceleration or suppression is sensitive to the functional form chosen to fit to the data, making it difficult to draw decisive conclusions. This suggests new methods are needed that do not require a functional form to be chosen, and provide age‐dependent uncertainty bounds.

Description: Assessing the sensitivity of annual streamflow to precipitation is challenging due to the complexity of the processes that control the water balance. A low-dimensional model can be useful to interrogate data in regional assessments of a large number of catchments, and can provide insights into the broad similarities and differences between catchments' behaviors. This work assesses the sensitivity to precipitation of total annual streamflow, as well as its slow and fast flow components, within the framework of the Ponce and Shetty water balance model. This framework assumes that there are upper limits on the ability of a catchment to store and evaporate water, and there are minimum threshold amounts of precipitation and wetting (precipitation minus fast flow) needed to initiate fast and slow runoff. The flow elasticities (percent of change in flow per percent of change in annual precipitation) were estimated for 405 catchments in the Model-Parameter Estimation Experiment data set (including an assessment of parameter uncertainty). The elasticity of total discharge was 2.1 on average across the catchments, which is consistent with other studies. The fast component was higher (≈ 2.4) and slow flow was lower (≈ 2.0). Elasticities were highest and most variable in arid areas. The variations in elasticity between sites were shown to be primarily controlled by the two threshold parameters. The thresholds were a high proportion of mean annual precipitation in arid sites where only a small proportion of catchment wetting is released as slow flow. This provides some insight into previous observations that the sensitivity is correlated with climate.

Description: Watersheds can be characterized as complex space-time filters that transform incoming fluxes of energy, water, and nutrients into variable output signals. The behavior of these filters is driven by climate, geomorphology, and ecology and, accordingly, varies from site to site. We investigated this variation by exploring the behavior of evapotranspiration signals from 14 different AmeriFlux sites. Evapotranspiration is driven by water and energetic forcing and is mediated by ecology and internal redistribution of water and energy. As such, it integrates biological and physical controls, making it an ideal signature to target when investigating watershed filtering. We adopted a paradigmatic approach (referred to as the null model) that couples the Penman-Monteith equation to a soil moisture model and explored the deviations between the predictions of the null model and the observed AmeriFlux data across the sites in order to identify the controls on these deviations and their commonalities and differences across the sites. The null model reproduced evapotranspiration fluxes reasonably well for arid, shallow-rooted systems but overestimated the effects of water limitation and could not reproduce seasonal variation in evapotranspiration at other sites. Accounting for plant access to groundwater (or deep soil moisture) reserves and for the effects of soil temperature on limiting evapotranspiration resolved these discrepancies and greatly improved prediction of evapotranspiration at multiple time scales. The results indicate that site-specific hydrology and climatic factors pose important controls on biosphere-hydrosphere interactions and suggest that plant–water table interactions and early season phenological controls need to be incorporated into even simple models to reproduce the seasonality in evapotranspiration.

Description: Conceptualizing catchments as physicochemical filters is an appealing way to link streamflow discharge and concentration time series to hydrological and biogeochemical processing in hillslopes and drainage networks. Making these links explicit is challenging in complex watersheds but may be possible in highly modified catchments where hydrological and biogeochemical processes are simplified. Linking hydrological and biogeochemical filtering in highly modified watersheds is appealing from a water quality perspective in order to identify the major controls on chemical export at different spatial and temporal scales. This study investigates filtering using a 10 year data set of hydrological and biogeochemical export from a small (

Description: Temporal patterns of solute transport and transformation through the vadose zone are driven by the stochastic variability of water fluxes. This is determined by the hydrologic filtering of precipitation variability into infiltration, storage, drainage, and evapotranspiration. In this work we develop a framework for examining the role of the hydrologic filtering and, in particular, the effect of evapotranspiration in determining the travel time and delivery of sorbing, reacting solutes transported through the vadose zone by stochastic rainfall events. We describe a 1-D vertical model in which solute pulses are tracked as point loads transported to depth by a series of discrete infiltration events. Numerical solutions of this model compare well to the Richards equation–based HYDRUS model for some typical cases. We then utilize existing theory of the stochastic dynamics of soil water to derive analytical and semianalytical expressions for the probability density functions (pdf's) of solute travel time and delivery. The moments of these pdf's directly relate the mean and variance of expected travel times to the water balance and show how evapotranspiration tends to reduce (and make more uncertain) the mass of a degrading solute delivered to the base of the vadose zone. The framework suggests a classification of different modes hydrologic filtering depending on hydroclimatic and landscape controls. Results suggest that variability in travel times decreases with soil depth in wet climates but increases with soil depth in dry climates. In dry climates, rare large storms can be an important mechanism for leaching to groundwater.

Description: We evaluate the extent to which within-year rainfall variability controls interannual variability of catchment water balance. To this end, we analytically derive the probability density function of the annual Budyko evaporation index, B (i.e., the ratio of annual actual evapotranspiration to annual precipitation), by accounting for the stochastic nature of intra-annual rainfall fluctuation and neglecting all other sources of variability. We apply our analytical model to 424 catchments located in different climatic regions across the conterminous United States to perform this assessment. In general, we found that the model is capable of explaining mean B but is less accurate in predicting its coefficient of variation. Nonetheless, in a significant number of catchments the model can provide adequate predictions of the probability density function of B. Clear geographic patterns can be distinguished in the residuals between observed and predicted statistics of B. Interannual variability is thus not always associated with random intra-annual rainfall fluctuations. In some regions, other controls, such as seasonality and vegetation adaptations, are possibly more important. A sensitivity analysis of model parameters helped characterize the dominant controls on the distribution of B in terms of three dimensionless ratios that include climatic and soil characteristics. This study represents the first step in a diagnostic, data-driven analysis of the climatic controls on the interannual variability of catchment water balance.

Description: The models of stream reach hyporheic exchange that are typically used to interpret tracer data assume steady-flow conditions, and impose further assumptions about transport processes on the interpretation of the data. Here we show how rank StorAge Selection (rSAS) functions can be used to extract ‘process-agnostic’ information from tracer breakthrough curves about the time-varying turnover of reach storage. A sequence of seven slug injections was introduced to a small stream at baseflow over the course of a diel fluctuation in stream discharge, providing breakthrough curves at discharges ranging from 0.7 - 1.2 L/s. Shifted gamma distributions, each with three parameters varying stepwise in time, were used to model the rSAS function and calibrated to reproduce each breakthrough curve with Nash-Sutcliffe efficiencies in excess of 0.99. Variations in the fitted parameters over time suggested that storage within the reach does not uniformly increase its turnover rate when discharge increases. Rather, changes in transit time are driven by both changes in the average rate of turnover (external variability) and changes in the relative rate that younger and older water contribute to discharge (internal variability). Specifically, at higher discharge the turnover rate increased for the youngest part of the storage (corresponding to approximately 5 times the volume of the channel), while discharge from the older part of the storage remained steady, or declined slightly. The method is shown to be extensible as a new approach to modeling reach-scale solute transport that accounts for the time-varying, discharge-dependent turnover of reach storage. This article is protected by copyright. All rights reserved.