Virtual experiments: a new approach for improving process conceptualization in hillslope hydrology

Key words: Hillslope geometry, Hillslope hydrology, Hillslope stability, Complex hillslopes, Modeling shallow landslides, HSB model, HSB-SM model. The hydrologic response of a hillslope to rainfall involves a complex, transient saturated-unsaturated interaction that usually leads to a water table rise. An increase of saturated groundwater flow can act as the triggering mechanism for slope failure. To account for the three-dimensional hillslope shape in which the groundwater flow and storage processes take place, simple (low-dimensional) but physically realistic models that represent hydrological processes at the hillslope scales are needed for reliable simulation of hillslope stability at the landscape scale. In this thesis the focus is on investigating the relation between hillslope geometry, hillslope hydrology and slope stability in complex hillslopes and hollows. Several models have been presented in this thesis which examine the stability of nine characteristic hillslope types (landform elements) with three different profile curvatures (concave, straight and convex) and three different plan shapes (convergent, parallel and divergent). In addition to testing our models for nine characteristic hillslope types, a general relationship between plan shape and profile curvature of landform elements and the factor of safety is derived for a predefined hillslope length scale. Our results show that slope stability increases when profile curvature changes from concave to convex. In terms of plan shapes, changing from convergent to divergent, slope stability increases for all length profiles. Our analyses also show that the minimum safety factor occurs when the rate of subsurface flow is maximum. In fact, by increasing the subsurface flow, stability decreases for all hillslope shapes. Moreover, after a certain period of rainfall, the convergent hillslopes with concave and straight profiles become unstable faster than others whilst divergent convex hillslopes remain stable (even after intense rainfall). We also demonstrate that in hillslopes with non-constant soil depth (possible deep landslides), the ones with convex profiles and convergent plan shapes have slip surfaces with the minimum safety factor near the outlet region. Finally, we demonstrate that, in addition to bedrock slope, hillslope shape as represented by plan shape and profile curvature is an important control on hillslope stability. With respect to the relation between rainfall occurrence and slope instability, a probabilistic model of rainfall-induced shallow landslides in complex hollows is also presented to investigate the relation between return period of rainfall, deposit thickness and landslide occurrence. A long term analysis of shallow landslides by the presented model illustrates that all hollows show a quite different behavior from the stability view point. Finally, we conclude that incorporating a more realistic description of hollow hydrology (the hillslope-storage Boussinesq model instead of the kinematic wave model) in landslide probability models is necessary, especially for hollows with a high convergence degree, which are more susceptible to landsliding. This model helps to theoretically investigate the relationship between return period of rainfall and landslide occurrence related to soil production (deposit thickness) in complex hollows. In summary this thesis aims to understand theoretically how hydrological processes (subsurface flow and water table dynamics) affect slope stability in complex hillslopes and hollows. The presented models can widely be applied in many investigations of hillslope stability analysis because of their relative simplicity (low-dimensional).

<p>Subsurface structural heterogeneity can route soil water through the vadose zone in complex ways that are difficult to observe or model in detail. The fill-and-spill hypothesis, which was developed to explain observations from field experiments at the hillslope scale, suggests that lateral flow at the soil-bedrock interface (or other permeability contrasts) is only activated once depressions in the microtopography of that interface become saturated and connect laterally. To reproduce this fill-and-spill phenomenon, a Richards equation-based numerical model would require a discretization of this morphology at a fine scale. A coarse representation smooths the interface eliminating the essential local storage-excess threshold behavior. However, the accuracy and abundance of field measurements rarely provide the data that would be needed to do this, and the fine discretization creates a high computational burden.</p><p>Here we explore the potential of an upscaled representation of the fill-and-spill mechanism based on parameterization of a permeability tensor with saturation-dependent anisotropy. By increasing empirical lateral hydraulic conductivity as they approach saturation, this anisotropy could reproduce how the fill-and-spill causes saturated patches at the permeability contrast to connect along preferential flow paths. Such a process representation could be incorporated into a Richards equation-based model enabling it to reproduce the fill-and-spill phenomenon even with a coarse spatial resolution.</p><p>We tested this idea using ParFlow to model virtual hillslopes with synthetic rugged internal topography. We then investigated the effective permeability tensor over an averaging volume that encloses the interface. By parameterizing the anisotropy of an interface block under changing moisture variables, we may be able to generate predictions of how the fine-scale fill-and-spill processes integrate to the hillslope and catchment scale.</p>

Subsurface flow is a prominent runoff process in sloping lands of purple soil in the upper Yangtze River basin. However, it remains difficult to identify and quantify. In this study, in situ runoff experimental plots were used to measure soil moisture dynamics using an array of time domain reflectometry (TDR) together with overland flow and subsurface flow using isolated collecting troughs. Frequency of preferential flow during rainfall events and the controls of subsurface flow processes were investigated through combined analysis of soil properties, topography, rainfall intensity, initial wetness, and tillage. Results showed that subsurface flow was ubiquitous in purple soil profiles due to well-developed macropores, especially in surface soils while frequency of preferential flow occurrence was very low (only 2 cases in plot C) during all 22 rainfall events. Dry antecedent moisture conditions promoted the occurrence of preferential flow. However, consecutive real-time monitoring of soil moisture at different depths and various slope positions implied the possible occurrence of multiple subsurface lateral flows during intensive storms. Rainfall intensity, tillage operation, and soil properties were recognized as main controls of subsurface flow in the study area, which allows the optimization of management practices for alleviating adverse environmental effects of subsurface flow in the region.

Research on the effects of vegetation manipulation on snowpack, soil water, and streamwater chemistry and flux has been underway at the Fraser Experimental Forest (FEF), CO, since 1982. Greater than 95% of FEF snowmelt passes through watersheds as subsurface flow where soil processes significantly alter meltwater chemistry. To better understand the mechanisms accounting for annual variation in watershed streamwater ion concentration and flux with snowmelt, we studied subsurface water flow, its ion concentration, and flux in conterminous forested and clear cut plots. Repetitive patterns in subsurface flow and chemistry were apparent. Control plot subsurface flow chemistry had the highest ion concentrations in late winter and fall. When shallow subsurface flow occurred, its Ca 2+ , SO 4 and HCO 3 - concentrations were lower and K + higher than deep flow. The percentage of Ca 2+ , NO SO 4 2- , and HCO 3 - flux in shallow depths was less and K + slightly greater than the percentage of total flow. Canopy removal increased precipitation reaching the forest floor by about 40%, increased peak snowpack water equivalent (SWE) > 35%, increased the average snowpack Ca 2+ , NO 3 - , and NH 4 + content, reduced the snowpack K + content, and increased the runoff four-fold. Clear cutting doubled the percentage of subsurface flow at shallow depths, and increased K + concentration in shallow subsurface flow and NO 3 - concentrations in both shallow and deep flow. The percentage change in total Ca 2+ , SO 4 2- , and HCO 3 - flux in shallow depths was less than the change in water flux, while that of K + and NO 3 - flux was greater. Relative to the control, in the clear cut the percentage of total Ca 2+ flux at shallow depths increased from 5 to 12%, SO 4 2- 5.4 to 12%, HCO 3 - from 5.6 to 8.7%, K + from 6 to 35%, and NO 3 - from 2.7 to 17%. The increases in Ca 2+ and SO 4 2- flux were proportional to the increase in water flux, the flux of HCO 3 - increased proportionally less than water flux, and NO 3 - and K + were proportionally greater than water flux. Increased subsurface flow accounted for most of the increase in non-limiting nutrient loss. For limiting nutrients, loss of plant uptake and increased shallow subsurface flow accounted for the greater loss. Seasonal ion concentration patterns in streamwater and subsurface flow were similar.

Dividing a catchment to subcatchment or hillslope scales allows for better scrutiny of the changes in spatial distribution of rainfall, soil attributes and plant cover across the catchment. An instantaneous unit hydrograph model is suggested for simulating runoff hydrographs for complex hillslopes. This model is able to estimate surface and subsurface flows of the catchment based on the Dunne-Black mechanism. For this purpose, a saturation model is used to separate the saturated and unsaturated zones in complex hillslopes. The profile curvatures (concave, straight and convex) and plan shapes (convergent, parallel and divergent) of complex hillslopes are considered, in order to compute the travel time of surface and subsurface flows. The model was used for prediction of the direct runoff hydrograph and subsurface flow hydrograph of Walnut Gulch No. 125 catchment in Arizona (USA). Based on results, the geometry of hillslopes can change the peak of the direct runoff hydrograph up to two-fold, either higher or lower. The divergent hillslopes show higher peaks in comparison with the parallel and convergent hillslopes. The highest and lowest peak flows correspond to divergent-concave and convergent-straight hillslopes, respectively.

Despite considerable research performed on forested catchments in the Ouachita Mountains of Oklahoma and Arkansas, little information on hydrological processes in operation is available. Based on catchment physical characteristics, subsurface flow was thought to be an important hydrological process in the region. Therefore, this study was undertaken to determine the occurrence, rates, timing and volumes of subsurface flow, and to estimate the importance of subsurface flow as a streamflow generating process. Subsurface flow was collected from three hillslope sites on a 7.7 ha forested catchment. Hillslope sites drained through natural seepage faces located near stream channels. Subsurface flow was collected from three depths at each hillslope site, below the litter layer, below the a horizon, and within the B horizon (Bt21). Subsurface flow occurred and was measured during 11 of 31 rainfall events. Subsurface flow responded rapidly to the initiation of and to changes in intensity of rainfall at all depths. the rapid response was indicative of flow through soil macropores. B horizon subsurface flow commenced within 10 to 180 min of the initiation of rainfall. Multiple linear regression showed that the volume of subsurface flow generated during a given storm was directly related to rainfall depth and a 7‐day antecedent precipitation index used to represent antecedent water content. About 67 per cent of the total subsurface flow collected during the study was produced in one large storm under wet antecedent conditions. the storm was equal to the 2‐year, 24‐hour storm for the region. Measured subsurface flow volumes were extended to the watershed scale to provide estimates of catchment‐wide contributions to streamflow. It was estimated that subsurface flow contributed from 1 to 48 per cent of total quickflow measured at the catchment outlet. Based on the timing of subsurface flow, it was estimated that subsurface flow May, contribute up to 70 per cent of quickflow before and soon after peak flow.

Agricultural managed aquifer recharge (AgMAR) is a strategy whereby surface water is used to intentionally flood croplands to recharge underlying aquifers. However, nitrate (NO3−) contamination in agriculturally intensive regions poses a threat to groundwater resources under AgMAR. We use a reactive transport model to understand the effects of AgMAR management strategies (i.e., by varying the frequency, duration between flooding events, and amount of water) on NO3− leaching to groundwater under different stratigraphic configurations and antecedent moisture conditions. We examine the potential of denitrification and nitrogen retention in deep vadose zone sediments (∼15 m) using variable AgMAR application rates on two‐dimensional representations of differently textured soils, soils with discontinuous bands/channels, and with preferential flow paths characteristic of agricultural fields. Simulations indicate finer textured sediments, alone or embedded within/adjacent to high flow regions, are important reducing zones providing conditions needed for denitrification. Simulation results suggest that applying water all‐at‐once rather than in increments transports higher concentrations of NO3− deeper into the profile, which may exacerbate groundwater quality. This transport into deeper depths can be aggravated by wetter antecedent soil moisture conditions. However, applying water all‐at‐once also increases denitrification within the vadose zone by promoting anoxic conditions. We conclude that AgMAR can be designed to enhance denitrification in the subsurface and reduce NO3− leaching to groundwater, while specifically accounting for lithologic heterogeneity, antecedent soil moisture conditions, and depth to the water table. Our findings are potentially relevant to other systems that experience flooding inundation such as floodplains and dedicated recharge basins.

This work deals with a rearrangement of Richards Equation to obtain a better understanding of the components of the subsurface water and pressure flows and their interactions in a hillslope. The basic idea proposed in this paper is the normalization of the spatial and temporal coordinates according to the physical knowledge of the processes and the geometry of a hillslope. The pressure head and all the other quantities contained in Richards Equation are rescaled to obtain a dimensionless equation. The pressure head is also split into an equilibrium component and a transient component and expanded in a perturbation series. Subsequently, Richards Equation itself is conveniently split into two equations connected by a source/sink term. Results of these manipulations show that, for the first order approximation, the water and pressure flow is slope‐normal, while slope‐parallel effects only occur at successive orders. Integrating the perturbed equation obtained for the long‐term pressure head component results in the well‐known Boussinesq Equation for the water table level. Further integrations then lead to the hillslope‐storage Boussinesq model and finally to a generalization of the O'Loughlin formula for the slope‐parallel long‐term subsurface flow. The introduced source/sink term is estimated at the first order of approximation to be proportional to the temporal variation of water pressure head at the bottom of the integration domain. The treatment of the equations clarifies some of the mechanisms acting in water pressure redistribution at hillslope scale, even without solving the equation.

Key words: hillslope hydrology, low-dimensional modeling, Boussinesq equation, Richards equation, water table dynamics.In this thesis the focus is on investigating the hillslope hydrological behavior, as a crucial part in understanding the catchment hydrological response. To overcome difficulties associated with most of the existing models, i.e., high computational costs and difficulties in model parameterization and calibration, the focus is on low-dimensional physically based models. The central question is whether it is possible to formulate low-dimensional physically based models such that the essential physical behavior of the natural system is preserved.Several models are compared to each other and to measurements from a laboratory and from a field site. The comparisons are carried out for a diversity of bedrock slopes, hillslope shapes, and profile curvatures. The low-dimensional models that are formulated are essentially based on the hillslope-storage Boussinesq (HSB) model. Several modifications to the model are conducted in order to investigate the model response under different conditions: a) a generalized HSB formulation is derived that allows model evaluation on curved bedrock profiles, b) a new HSB model is derived in which the effects of capillarity are partly accounted for based on the assumption of hydraulic equilibrium in the unsaturated zone, and c) a coupled saturated-unsaturated HSB model is derived in which the unsaturated zone dynamics are described with a one-dimensional Richards model. Evaluation of the developed low-dimensional models generally shows that: a) the HSB model saturated zone dynamics alone can describe the outflow rates and water table dynamics accurately when the influence of capillarity is small; b) for very shallow soils or water tables in the proximity of the soil surface, the effects of capillarity are more clearly noticeable and it is possible to improve the simulated water table dynamics during drainage experiments significantly by regarding the parameter drainable porosity as a state-dependent parameter of which the value depends on the unsaturated depth; c) for drainage and recharge scenario's, a low-dimensional coupled saturated-unsaturated model that is developed to dynamically account for the unsaturated zone processes is very well capable of describing outflow rates and water table dynamics; d) the comparison of the results of the coupled model run in an uncalibrated mode to field data yields a reasonable match in terms of hydrographs and water table dynamics. However, the water table response is highly sensitive due to limited free pore space caused by capillarity effects.

The fate and transport of contaminants in the vicinity of septic fields remains poorly understood in many hydrogeomorphological environments. We report hydrometric data from an intensive hillslope‐scale experiment conducted between 29 August and 11 November 1998 at a residential leach field in New York State. The objective of our study was to characterize water flux within the vadose zone, understand the physical controls on the flux, and predict how this ultimately will affect subsurface water quality. Soil‐water flux was calculated using matric potential measurements from a network of 25 tensiometer nests, each nest consisting of three tensiometers installed to depths of 10, 50 and 130 cm. Unsaturated hydraulic conductivity curves were derived at each depth from field‐determined time‐domain reflectometry–tensiometry moisture‐release curves and borehole permeametry measurements. Flownets indicated that a strong upward flux of soil water occurred between rainstorms. Following the onset of (typically convective) rainfall, low near‐surface matric potentials were rapidly converted to near‐saturated and saturated conditions, promoting steep vertical gradients through the near‐surface horizons of the hillslope. Lateral hydraulic gradients were typically 10 times smaller than the vertical gradients. Resultant flow vectors showed that the flux was predominantly vertical through the vadose zone, and that the flux response to precipitation was short‐lived. The flux response was controlled primarily by the shape of the unsaturated hydraulic conductivity curves, which indicated a rapid loss of conductivity below saturation. Thus, soil water had a very high residence time in the vadose zone. The absence of rapid wetting at 130 cm and the delayed and small phreatic zone response to rainfall indicated that water movement through macropores did not occur on this hillslope. These results are consistent with a Cl tracing experiment, which demonstrated that the tracer was retained in the vadose zone for several months after injection to the system. Copyright © 2002 John Wiley & Sons, Ltd.

Hillslope dynamics modeled with increasing complexity

Hillslopes are fundamental landscape units that strongly control the processes whereby precipitation or snowmelt is vertically and laterally transported to the streams. They are, in a sense, microcosms of catchments. Understanding and predicting the hillslope response is highly important in terms of flood prediction, transport of nutrients and sediments into surface water bodies, slope stability, and soil-atmosphere-vegetation exchange processes. Through numerous field experiments and numerical studies, much progress has been made in hillslope hydrology in the past decades. However, our ability to extrapolate these findings to ungauged hillslopes and catchments is still very poor (Sivapalan 2005). A common thread that has evolved recently is to search for the underlying principles of hydrological processes instead of characterizing and cataloging the enormous heterogeneity and complexity of rainfall-runoff processes (McDonnell et al. 2007). The aim of this chapter is to provide an overview on today’s conceptual models of processes at the hillslope scale and to examine the factors driving these mechanisms. The focus will be on compiling recent findings on the dominant controls of hillslope runoff processes to meet the need of identifying underlying principles. The chapter closes with thoughts on new dimensions and directions of hillslope hydrology and research avenues to follow for the future.

Identification of mechanical responses of steel sheets under non-proportional loadings using dislocation-density based crystal plasticity model

Abstract. Rainfall-runoff response in temperate humid headwater catchments is mainly controlled by hydrological processes at the hillslope scale. Applied tracer experiments with fluorescent dye and salt tracers are well known tools in groundwater studies at the large scale and vadose zone studies at the plot scale, where they provide a means to characterise subsurface flow. We extend this approach to the hillslope scale to investigate saturated and unsaturated flow paths concertedly at a forested hillslope in the Austrian Alps. Dye staining experiments at the plot scale revealed that cracks and soil pipes function as preferential flow paths in the fine-textured soils of the study area, and these preferential flow structures were active in fast subsurface transport of tracers at the hillslope scale. Breakthrough curves obtained under steady flow conditions could be fitted well to a one-dimensional convection-dispersion model. Under natural rainfall a positive correlation of tracer concentrations to the transient flows was observed. The results of this study demonstrate qualitative and quantitative effects of preferential flow features on subsurface stormflow in a temperate humid headwater catchment. It turns out that, at the hillslope scale, the interactions of structures and processes are intrinsically complex, which implies that attempts to model such a hillslope satisfactorily require detailed investigations of effective structures and parameters at the scale of interest.

A hybrid coupled model of surface and subsurface flow for surface irrigation