Physically based modelling of sheet erosion (detachment and deposition processes) in complex hillslopes

A one‐dimensional uncoupled model governed by this research is a physics‐based modelling of the rainfall‐runoff induced erosion process. The presented model is composed of three parts of a three‐dimensional (3D) hillslope geometry, a nonlinear storage (kinematic wave) model for hillslope hydrological response, and an unsteady physically based surface erosion model. The 3D hillslope geometry model allows describing of the hillslope morphology by defining their plan shape and profile curvature. By changing these two topographic parameters, nine basic hillslope types are derived. The modelling of hillslope hydrological response is based on a flow continuity equation as the relation of discharge and flow depth is passed on kinematic wave approximation. The erosion model is based on a mass conservation equation for unsteady flow. The model assumes that suspended sediment does not affect flow dynamics. The model also accounts for the effect of flow depth plus loose soil depth on soil detachment. The presented model was run for two different precipitations, slope content, and length, and results were plotted for sediment detachment/deposition rate. Based on the obtained results, in hillslopes with convex and straight profile curvatures, sediment detachment only occurred in the whole length of the hillslope. However, in concave ones, sediment detachment and deposition only occurred together in hillslope. The hillslopes with straight profiles and convergent plans have the highest rate of detachment. Also, results show that most detachment rates occur in convex profile curvatures, which are about 15 times more than in straight profiles. Copyright © 2015 John Wiley & Sons, Ltd.     

A numerical investigation of bedrock groundwater recharge and exfiltration on soil mantled hillslopes

Here we use Richards Equation models of variably saturated soil and bedrock groundwater flow to investigate first-order patterns of the coupling between soil and bedrock flow systems. We utilize a Monte Carlo sensitivity analysis to identify important hillslope parameters controlling bedrock recharge and then model the transient response of bedrock and soil flow to seasonal precipitation. Our results suggest that hillslopes can be divided into three conceptual zones of groundwater interaction, (a) the zone of lateral unsaturated soil moisture accumulation (upper portion of hillslope), (b) the zone of soil saturation and bedrock recharge (middle of hillslope) and (c) the zone of saturated-soil lateral flow and bedrock groundwater exfiltration (bottom of hillslope). Zones of groundwater interaction expand upslope during periods of precipitation and drain downslope during dry periods. The amount of water partitioned to the bedrock groundwater system a can be predicted by the ratio of bedrock to soil saturated hydraulic conductivity across a variety of hillslope configurations. Our modelled processes are qualitatively consistent with observations of shallow subsurface saturation and groundwater fluctuation on hillslopes studied in our two experimental watersheds and support a conceptual model of tightly coupled shallow and deep subsurface circulation where groundwater recharge and discharge continuously stores and releases water from longer residence time storage.     

A low‐dimensional hillslope‐based catchment model for layered groundwater flow

Despite the strong interaction between surface and subsurface waters, groundwater flow representation is often oversimplified in hydrological models. For instance, the interplay between local or shallow aquifers and deeper regional‐scale aquifers is typically neglected. In this work, a novel hillslope‐based catchment model for the simulation of combined shallow and deep groundwater flow is presented. The model consists of the hillslope‐storage Boussinesq (hsB) model representing shallow groundwater flow and an analytic element (AE) model representing deep regional groundwater flow. The component models are iteratively coupled via a leakage term based on Darcy's law, representing delayed recharge to the regional aquifer through a low conductivity layer. Simulations on synthetic single hillslopes and on a two‐hillslope open‐book catchment are presented, and the results are compared against a benchmark three‐dimensional Richards equation model. The impact of hydraulic conductivity, hillslope plan geometry (uniform, convergent, divergent), and hillslope inclination (0.2%, 5%, and 30%) under drainage and recharge conditions are examined. On the single hillslopes, good matches for heads, hydrographs, and exchange fluxes are generally obtained, with the most significant differences in outflows and heads observed for the 30% slope and for hillslopes with convergent geometry. On the open‐book catchment, cumulative outflows are overestimated by 1–4%. Heads in the confined and unconfined aquifers are adequately reproduced throughout the catchment, whereas exchange fluxes are found to be very sensitive to the hillslope drainable porosity. The new model is highly efficient computationally compared to the benchmark model. The coupled hsB/AE model represents an alternative to commonly used groundwater flow representations in hydrological models, of particular appeal when surface–subsurface exchanges, local aquifer–regional aquifer interactions, and low flows play a key role in a watershed's dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Snowmelt runoff and soil moisture dynamics on steep subalpine hillslopes

Snowmelt water supplies streamflow and growing season soil moisture in mountain regions, yet pathways of snowmelt water and their effects on moisture patterns are still largely unknown. This study examined how flow processes during snowmelt runoff affected spatial patterns of soil moisture on two steep sub‐alpine hillslope transects in Rocky Mountain National Park, CO, USA. The transects have northeast‐facing and east‐facing aspects, and both extend from high‐elevation bedrock outcrops down to streams in valley bottoms. Spatial patterns of both snow depth and near‐surface soil moisture were surveyed along these transects in the snowmelt and summer seasons of 2008–2010. To link these patterns to flow processes, soil moisture was measured continuously on both transects and compared with the timing of discharge in nearby streams. Results indicate that both slopes generated shallow lateral subsurface flow during snowmelt through near‐surface soil, colluvium and bedrock fractures. On the northeast‐facing transect, this shallow subsurface flow emerged through mid‐slope seepage zones, in some cases producing saturation overland flow, whereas the east‐facing slope had no seepage zones or overland flow. At the hillslope scale, earlier snowmelt timing on the east‐facing slope led to drier average soil moisture conditions than on the northeast‐facing slope, but within hillslopes, snow patterns had little relation to soil moisture patterns except in areas with persistent snow drifts. Results suggest that lateral flow and exfiltration processes are key controls on soil moisture spatial patterns in this steep sub‐alpine location. Copyright © 2014 John Wiley & Sons, Ltd.     

Parametric study of a physically-based,plot-scale hillslope hydrological model through virtual experiments

Abstract

A physically-based hillslope hydrological model with shallow overland flow and rapid subsurface stormflow components was developed and calibrated using field experiments conducted on a preferential path nested hillslope in northeast India. Virtual experiments were carried out to perform sensitivity analysis of the model using the automated parameter estimation (PEST) algorithm. Different physical parameters of the model were varied to study the resulting effects on overland flow and subsurface stormflow responses from the theoretical hillslopes. It was observed that topographical shapes had significant effects on overland flow hydrographs. The slope profiles, surface storage, relief, rainfall intensity and infiltration rates primarily controlled the overland flow response of the hillslopes. Prompt subsurface stormflow responses were mainly dominated by lateral preferential flow, as soil matrix flow rates were very slow. Rainfall intensity and soil macropore structures were the most influential parameters on subsurface stormflow. The number of connected soil macropores was a more sensitive parameter than the size of macropores. In hillslopes with highly active vertical and lateral preferential pathways, saturation excess overland flow was not evident. However, saturation excess overland flow was generated if the lateral macropores were disconnected. Under such conditions, rainfall intensity, duration and preferential flow rate governed the process of saturation excess overland flow generation from hillslopes.

Editor D. Koutsoyiannis; Associate editor C. Perrin     

Hydrogeological response to climate change in alpine hillslopes

Climate change threatens water resources in snowmelt‐dependent regions by altering the fraction of snow and rain and spurring an earlier snowmelt season. The bulk of hydrological research has focused on forecasting response in streamflow volumes and timing to a shrinking snowpack; however, the degree to which subsurface storage offsets the loss of snow storage in various alpine geologic settings, i.e. the hydrogeologic buffering capacity, is still largely unknown. We address this research need by assessing the affects of climate change on storage and runoff generation for two distinct hydrogeologic settings present in alpine systems: a low storage granitic and a greater storage volcanic hillslope. We use a physically based integrated hydrologic model fully coupled to a land surface model to run a base scenario and then three progressive warming scenarios, and account for the shifts in each component of the water budget. For hillslopes with greater water retention, the larger storage volcanic hillslope buffered streamflow volumes and timing, but at the cost of greater reductions in groundwater storage relative to the low storage granite hillslope. We found that the results were highly sensitive to the unsaturated zone retention parameters, which in the case of alpine systems can be a mix of matrix or fracture flow. The presence of fractures and thus less retention in the unsaturated zone significantly decreased the reduction in recharge and runoff for the volcanic hillslope in climate warming scenarios. This approach highlights the importance of incorporating physically based subsurface flow in to alpine hydrology models, and our findings provide ways forward to arrive at a conceptual model that is both consistent with geology and hydrologic principles. Copyright © 2016 John Wiley & Sons, Ltd.     

Effects of hillslope topography on hydrological responses in a weathered granite mountain,Japan: comparison of the runoff response between the valley‐head and the side slope

To evaluate the effects of hillslope topography on storm runoff in a weathered granite mountain, discharge rate, soil pore water pressures, and water chemistry were observed on two types of hillslope: a valley‐head (a concave hillslope) and a side slope (a planar hillslope). Hydrological responses on the valley‐head and side slope reflected their respective topographic characteristics and varied with the rainfall magnitude. During small rainfall events (<35 mm), runoff from the side slope occurred rapidly relative to the valley‐head. The valley‐head showed little response in storm runoff. As rainfall amounts increased (35–60 mm), the valley‐head yielded a higher flow relative to the side slope. For large rainfall events (>60 mm), runoff from both hillslopes increased with rainfall, although that from the valley‐head was larger than that from the side slope. The differences in the runoff responses were caused by differences in the roles of lower‐slope soils and the convergence of the hillslope. During small rainfall events, the side slope could store little water; in contrast, all rainwater could be stored in the soils at the valley‐head hollow. As the amount of rainfall increased, the subsurface saturated area of the valley‐head extended from the bottom to the upper portion of the slope, with the contributions of transient groundwater via lateral preferential flowpaths due to the high concentration of subsurface water. Conversely, saturated subsurface flow did not contribute to runoff responses, and the subsurface saturated area at the side slope did not extend to the upper slope for the same storm size. During large rainfall events, expansion of the subsurface saturated area was observed in both hillslopes. Thus, differences in the concentration of subsurface water, reflecting hillslope topography, may create differences in the extension of the subsurface saturated area, as well as variability in runoff responses. Copyright © 2007 John Wiley & Sons, Ltd.     

A low‐dimensional model of bedrock weathering and lateral flow coevolution in hillslopes: 2. Controls on weathering and permeability profiles,drainage hydraulics,and solute export pathways

The advance of a chemical weathering front into the bedrock of a hillslope is often limited by the rate weathering products that 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 coevolution 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.     

Analysis of hysteretic behaviour of a hillslope-storage kinematic wave model for subsurface flow

The objective of this work is to analyse the storage–flux hysteretic behaviour of a simplified model for subsurface flow processes. The subsurface flow dynamics is analysed by means of a model based on the kinematic wave assumptions and by using a width weighting/depth averaging scheme which allows to map the three-dimensional soil mantle into a one-dimensional profile. Continuity and a kinematic form of Darcy’s law lead to a hillslope-storage kinematic wave equation for subsurface flow, solvable with the method of characteristics. Adopting a second order polynomial function to describe the bedrock slope and an exponential function to describe the variation of the width of the hillslope with hillslope distance, we derive general solutions to the hillslope-storage kinematic wave equations, applicable to a wide range of hillslopes. These solutions provide a physical basis for deriving two geometric parameters α and ψ which define the hydrological similarity between hillslopes with respect to their characteristic response and hysteresis. The hysteresis η, quantified by the area of the hysteretic dimensionless loop, has been therefore computed for a range of values of parameters α and ψ. Slopes exhibit generally clockwise hysteretic loop in the flux-storage plot, with higher groundwater mean volume for given discharge on rising limb than at same discharge on falling limb. It has been found that hysteresis increases with decreasing α and ψ, i.e. with increasing convergence (for the shape) and concavity (for the profile), and vice versa. For relatively large values of α and ψ the hysteresis may take a complex pattern, with combination of clockwise to anticlockwise loop cycles. Application of the theory to three hillslopes in the Eastern Italian Alps provides an opportunity to examine how natural topographies are represented by the two hillslope hydrological similarity parameters.     

Subsurface lateral flow generation in aspen and conifer‐dominated hillslopes of a first order catchment in northern Utah

Mountain headwater catchments in the semi‐arid Intermountain West are important sources of surface water because these high elevations receive more precipitation than neighboring lowlands. This study examined subsurface runoff in two hillslopes, one aspen dominated, the other conifer dominated, adjacent to a first order stream in snow‐driven northern Utah. Snow accumulation, soil moisture, trenchflow and streamflow were examined in hillslopes and their adjacent stream. Snow water equivalents (SWEs) were greater under aspen stands compared to conifer, the difference increasing with higher annual precipitation. Semi‐variograms of shallow spatial soil moisture patterns and transects of continuous soil moisture showed no increase in soil moisture downslope, suggesting the absence of subsurface flow in shallow (～12 cm) soil layers of either vegetation type. However, a clear threshold relationship between soil moisture and streamflow indicated hillslope–stream connectivity, deeper within the soil profile. Subsurface flow was detected at ～50 cm depth, which was sustained for longer in the conifer hillslope. Soil profiles under the two vegetation types varied, with deep aspen soils having greater water storage capacity than shallow rocky conifer soils. Though SWEs were less under the conifers, the soil profile had less water storage capacity and produced more subsurface lateral flow during the spring snowmelt. Copyright © 2010 John Wiley & Sons, Ltd.     

Spatio‐temporal variability of piezometric response on two steep alpine hillslopes

Information on the main drivers of subsurface flow generation on hillslopes of alpine headwater catchments is still missing. Therefore, the dominant factors controlling the water table response to precipitation at the hillslope scale in the alpine Bridge Creek Catchment, Northern Italy, were investigated. Two steep hillslopes of similar size, soil properties and vegetation cover but contrasting topography were instrumented with 24 piezometric wells. Sixty‐three (63) rainfall‐runoff events were selected over three years in the snow‐free months to analyse the influence of rainfall depth, antecedent moisture conditions, hillslope topographic characteristics and soil depth on shallow water table dynamics. Piezometric response, expressed as percentage of well activation and water peak magnitude, was strongly correlated with soil moisture status, as described by an index combining antecedent soil moisture and rainfall depth. Hillslope topography was found to be a dominant control only for the convex‐divergent hillslope and during wet conditions. Timing of water table response depended primarily on soil depth and topographic position, with piezometric peak response occurring later and showing a greater temporal variability at the hillslope bottom, characterized by thicker soil. The relationship between mean hillslope water table level and standard deviation for all wells reflected the timing of the water table response at the different locations along the hillslopes. The outcomes of this research contribute to a better understanding of the controls on piezometric response at the hillslope scale in steep terrain and its role on the hydrological functioning of the study catchment and of other sites with similar physiographic characteristics. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic domain kinematic modelling for predicting interflow over leaky impeding layers

Traditional Boussinesq or kinematic simulations of interflow (i.e., lateral subsurface flow) assume no leakage through the impeding layer and require a no-flow boundary condition at the ridge top. However, recent analyses of many interflow-producing landscapes indicate that leaky impeding layers are common, that most interflow percolates well before reaching the toe slope, and therefore, the downslope contributing length is shorter than the hillslope length. In watersheds characterised by perched interflow over a low conductivity layer through permeable topsoil, interflow with percolation may be modelled with a kinematic wave model using a mobile upslope boundary condition defining the hillslope portion contributing interflow to valleys. Here, we developed and applied a dynamic interflow model to simulate interflow using a downslope travel distance concept such that only the active contributing length is modelled at any time. The model defines a variable active area based on the depth of the perched layer, the topographic slope and the ratio of the hydraulic conductivity of topsoil to that of the impeding layer. It incorporates a two-layer soil moisture accounting water balance analysis, a pedo-transfer function, and percolation and evaporation routines to predict interflow rates in continuous and event-based scenarios. We tested the modelling concept on two sets of data (2-year dataset of rainfall observations for the continuous simulation and a multi-day irrigation experiment for the event simulation) from a 121-m-long open interflow collection trench on an experimental hillslope at the Savannah River Site, South Carolina. The continuous model simulation partially represented the observed interflow hydrograph and perched water depth in the experimental hillslope with correlation coefficients of 0.85 and 0.35, respectively. Model performance improved significantly at event-scale analysis. The modelling approach realistically represents interflow dynamics in hillslopes with leaky impeding layers and can be integrated into catchment-scale hydrology models for more detailed hillslope process modelling.     

Physically‐based modelling of double‐peak discharge responses at Slapton Wood catchment

Heavy winter rainfall produces double‐peak hydrographs at the Slapton Wood catchment, Devon, UK. The first peak is saturation‐excess overland flow in the hillslope hollows and the second (i.e. the delayed peak) is subsurface stormflow. The physically‐based spatially‐distributed model SHETRAN is used to try to improve the understanding of the processes that cause the double peaks. A three‐stage (multi‐scale) approach to calibration is used: (1) water balance validation for vertical one‐dimensional flow at arable, grassland and woodland plots; (2) two‐dimensional flow for cross‐sections cutting across the stream valley; and (3) three‐dimensional flow in the full catchment. The main data are for rainfall, stream discharge, evaporation, soil water potential and phreatic surface level. At each scale there was successful comparison with measured responses, using as far as possible parameter values from measurements. There was some calibration but all calibrated values at one scale were used at a larger scale. A large proportion of the subsurface runoff enters the stream from three dry valleys (hillslope hollows), and previous studies have suggested convergence of the water in the three large hollows as being the major mechanism for the production of the delayed peaks. The SHETRAN modelling suggests that the hillslopes that drain directly into the stream are also involved in producing the delayed discharges. The model shows how in the summer most of the catchment is hydraulically disconnected from the stream. In the autumn the catchment eventually ‘wets up’ and shallow subsurface flows are produced, with water deflected laterally along the soil‐bedrock interface producing the delayed peak in the stream hydrograph. Copyright © 2007 John Wiley & Sons, Ltd.     

How to model shallow water‐table depth variations: the case of the Kervidy‐Naizin catchment,France

The aim of this work is threefold: (1) to identify the main characteristics of water‐table variations from observations in the Kervidy‐Naizin catchment, a small catchment located in western France; (2) to confront these characteristics with the assumptions of the Topmodel concepts; and (3) to analyse how relaxation of the assumptions could improve the simulation of distributed water‐table depth. A network of piezometers was installed in the Kervidy‐Naizin catchment and the water‐table depth was recorded every 15 min in each piezometer from 1997 to 2000. From these observations, the Kervidy‐Naizin groundwater appears to be characteristic of shallow groundwaters of catchments underlain by crystalline bedrock, in view of the strong relation between water distribution and topography in the bottom land of the hillslopes. However, from midslope to summit, the water table can attain a depth of many metres, it does not parallel the topographic surface and it remains very responsive to rainfall. In particular, hydraulic gradients vary with time and are not equivalent to the soil surface slope. These characteristics call into question some assumptions that are used to model shallow lateral subsurface flow in saturated conditions. We investigate the performance of three models (Topmodel, a kinematic model and a diffusive model) in simulating the hourly distributed water‐table depths along one of the hillslope transects, as well as the hourly stream discharge. For each model, two sets of parameters are identified following a Monte Carlo procedure applied to a simulation period of 2649 h. The performance of each model with each of the two parameter sets is evaluated over a test period of 2158 h. All three models, and hence their underlying assumptions, appear to reproduce adequately the stream discharge variations and water‐table depths in bottom lands at the foot of the hillslope. To simulate the groundwater depth distribution over the whole hillslope, the steady‐state assumption (Topmodel) is quite constraining and leads to unacceptable water‐table depths in midslope and summit areas. Once this assumption is relaxed (kinematic model), the water‐table simulation is improved. A subsequent relaxation of the hydraulic gradient (diffusive model) further improves water‐table simulations in the summit area, while still yielding realistic water‐table depths in the bottom land. Copyright © 2004 John Wiley & Sons, Ltd.     

Simulated effect of a forest road on near‐surface hydrologic response and slope stability

Forest management practices often result in significant changes to hydrologic and geomorphic responses at or near the earth's surface. A well‐known, but not fully tested, hypothesis in hillslope hydrology[sol ]geomorphology is that a near‐surface permeability contrast, caused by the surface compaction associated with forest roads, can result in diverted subsurface flow paths that produce increased up‐slope pore pressures and slope failure. The forest road focused on in this study is located in a steep forested, zero‐order catchment within the H. J. Andrews Experimental Forest (Oregon). A three‐phase modelling effort was employed to test the aforementioned hypothesis: (i) two‐dimensional (vertical slice), steady‐state, heterogeneous, saturated subsurface flow simulations at the watershed scale for establishing the boundary conditions for the catchment‐scale boundary‐value problem in (ii); (ii) two‐dimensional (vertical slice), transient, heterogeneous, variably saturated subsurface flow simulations at the catchment scale for estimating near‐surface hydrologic response and pore pressure distributions; and (iii) slope stability analyses, using the infinite slope approach, driven by the pore pressure distributions simulated in (ii), for assessing the impact of the forest road. Both observed and hypothetical rainfall events are used to drive the catchment‐scale simulations. The results reported here support the hypothesis that a forest road can have an effect on slope stability. The permeability contrast associated with the forest road in this study led to a simulated altering of slope‐parallel subsurface flow with increased pore pressures up‐slope of the road and, for a large rainfall event, a slope failure prediction. Copyright © 2005 John Wiley & Sons, Ltd.     

How well can the subsurface storage–discharge relation be interpreted and predicted using the geometric factors in headwater areas?

Headwater storage–discharge (S–Q) remains one of the least understood processes, and there is renewed interest in the S–Q relation. How well can the S–Q relation be interpreted mechanistically using geometric factors? In this paper, the hillslope storage Boussinesq and hillslope storage kinematic wave equation were adopted to guide the theoretical derivations. Analytical solutions were derived based on the hsKW equation for nine idealized hillslope aquifers, which were subdivided into two groups, i.e. hillslope aquifers with exponential hillslope width function (C1) and hillslope aquifers with Gaussian hillslope width function (C2). We found that analytical expressions of the S–Q relation can be derived for C1 hillslope aquifers. For more compound hillslope aquifers, i.e. C2, no explicit S–Q relation can be obtained. The whole subsurface recession after a rainstorm is simulated by applying the initial saturation condition. We found that the simulated S–Q processes can be characterized by a two‐phase recession, i.e. quick and slow recession. The time (t_b) at the dividing point of the quick and slow recessions depends on the geometric factors, such as the plan and profile curvature. In the quick recession for C1, many of the S–Q curves can be described as linear or quasi‐linear functions, which indicate that linear reservoir models can be applied approximately for recession simulations. However, during the slow recession phase of C1 and during the whole recession of C2, the S–Q relations are highly non‐linear. Finally, we compared the hillslope storage kinematic wave and hillslope storage Boussinesq models for simulating subsurface water recession after a rainstorm event in a real‐world headwater catchment (G5) in China. Through comparison of the recession slope curves, we found that the simulated results of the models employing the Gaussian hillslope width function match the observed hydrograph. The results indicated that appropriate organization of the hillslope geometric factors enhances our ability to make S–Q predictions. Copyright © 2016 John Wiley & Sons, Ltd.     

The sensitivity of hillslope bedrock erosion to precipitation

Decoupling the impacts of climate and tectonics on hillslope erosion rates is a challenging problem. Hillslope erosion rates are well known to respond to changes in hillslope boundary conditions (e.g. channel incision rates) through their dependence on soil thickness, and precipitation is an important control on soil formation. Surprisingly though, compilations of hillslope denudation rates suggest little precipitation sensitivity. To isolate the effects of precipitation and boundary condition, we measured rates of soil production from bedrock and described soils on hillslopes along a semi‐arid to hyperarid precipitation gradient in northern Chile. In each climate zone, hillslopes with contrasting boundary conditions (actively incising channels versus non‐eroding landforms) were studied. Channel incision rates, which ultimately drive hillslope erosion, varied with precipitation rather than tectonic setting throughout the study area. These precipitation‐dependent incision rates are mirrored on the hillslopes, where erosion shifts from relatively fast and biologically‐driven to extremely slow and salt‐driven as precipitation decreases. Contrary to studies in humid regions, bedrock erosion rates increase with precipitation following a power law, from ～1 m Ma^?1 in the hyperarid region to ～40 m Ma^?1 in the semi‐arid region. The effect of boundary condition on soil thickness was observed in all climate zones (thicker soils on hillslopes with stable boundaries compared to hillslopes bounded by active channels), but the difference in bedrock erosion rates between the hillslopes within a climate region (slower erosion rates on hillslopes with stable boundaries) decreased as precipitation decreased. The biotic‐abiotic threshold also marks the precipitation rate below which bedrock erosion rates are no longer a function of soil thickness. Our work shows that hillslope processes become sensitive to precipitation as life disappears and the ability of the landscape to respond to tectonics decreases. Copyright © 2010 John Wiley & Sons, Ltd.     

The exponential decline in saturated hydraulic conductivity with depth: a novel method for exploring its effect on water flow paths and transit time distribution

The strong vertical gradient in soil and subsoil saturated hydraulic conductivity is characteristic feature of the hydrology of catchments. Despite the potential importance of these strong gradients, they have proven difficult to model using robust physically based schemes. This has hampered the testing of hypotheses about the implications of such vertical gradients for subsurface flow paths, residence times and transit time distribution. Here we present a general semi‐analytical solution for the simulation of 2D steady‐state saturated‐unsaturated flow in hillslopes with saturated hydraulic conductivity that declines exponentially with depth. The grid‐free solution satisfies mass balance exactly over the entire saturated and unsaturated zones. The new method provides continuous solutions for head, flow and velocity in both saturated and unsaturated zones without any interpolation process as is common in discrete numerical schemes. This solution efficiently generates flow pathlines and transit time distributions in hillslopes with the assumption of depth‐varying saturated hydraulic conductivity. The model outputs reveal the pronounced effect that changing the strength of the exponential decline in saturated hydraulic conductivity has on the flow pathlines, residence time and transit time distribution. This new steady‐state model may be useful to others for posing hypotheses about how different depth functions for hydraulic conductivity influence catchment hydrological response. Copyright © 2016 John Wiley & Sons, Ltd.