- A.G.J. Hilberts (3)
- T.E. Huxman (1)
- E.E. Loon van (1)
- A.H. Loon van (1)
- L. Pangle (1)
- C. Paniconi (2)
- J.D. Pelletier (1)
- S.R. Saleska (1)
- A. Talebi (3)
- A.J. Teuling (1)
- P.A.A. Troch (5)
- P.A. Troch (3)
- R. Uijlenhoet (4)
- X. Zeng (1)
Hillslope-scale experiment demonstrates the role of convergence during two-step saturation
Gevaert, A. ; Teuling, A.J. ; Uijlenhoet, R. ; Delong, S. ; Huxman, T.E. ; Pangle, L. ; Breshears, D.D. ; Chorover, J. ; Pelletier, J.D. ; Saleska, S.R. ; Zeng, X. ; Troch, P.A.A. - \ 2014
Hydrology and Earth System Sciences 18 (2014). - ISSN 1027-5606 - p. 3681 - 3692.
groundwater ridging hypothesis - variable source areas - water-table response - streamflow generation - capillary-fringe - flow generation - subsurface flow - overland-flow - storm runoff - biosphere 2
Subsurface flow and storage dynamics at hillslope scale are difficult to ascertain, often in part due to a lack of sufficient high-resolution measurements and an incomplete understanding of boundary conditions, soil properties, and other environmental aspects. A continuous and extreme rainfall experiment on an artificial hillslope at Biosphere 2's Landscape Evolution Observatory (LEO) resulted in saturation excess overland flow and gully erosion in the convergent hillslope area. An array of 496 soil moisture sensors revealed a two-step saturation process. First, the downward movement of the wetting front brought soils to a relatively constant but still unsaturated moisture content. Second, soils were brought to saturated conditions from below in response to rising water tables. Convergent areas responded faster than upslope areas, due to contributions from lateral subsurface flow driven by the topography of the bottom boundary, which is comparable to impermeable bedrock in natural environments. This led to the formation of a groundwater ridge in the convergent area, triggering saturation excess runoff generation. This unique experiment demonstrates, at very high spatial and temporal resolution, the role of convergence on subsurface storage and flow dynamics. The results bring into question the representation of saturation excess overland flow in conceptual rainfall-runoff models and land-surface models, since flow is gravity-driven in many of these models and upper layers cannot become saturated from below. The results also provide a baseline to study the role of the co-evolution of ecological and hydrological processes in determining landscape water dynamics during future experiments in LEO.
A low-dimensional physically based model of hydrologic control of shallow landslinding on complex hillslopes
Talebi, A. ; Uijlenhoet, R. ; Troch, P.A. - \ 2008
Earth Surface Processes and Landforms 33 (2008)13. - ISSN 0197-9337 - p. 1964 - 1976.
storage boussinesq model - subsurface flow - debris flows - rainfall - slope - stability - soils
Hillslopes have complex three-dimensional shapes that are characterized by their plan shape, profile curvature of surface and bedrock, and soil depth. To investigate the stability of complex hillslopes (with different slope curvatures and plan shapes), we combine the hillslope-storage Boussinesq (HSB) model with the infinite slope stability method. The HSB model is based on the continuity and Darcy equations expressed in terms of storage along the hillslope. Solutions of the HSB equation account explicitly for plan shape by introducing the hillslope width function and for profile curvature through the bedrock slope angle and the hillslope soil depth function. The presented model is composed of three parts: a topography model conceptualizing three-dimensional soil mantled landscapes, a dynamic hydrology model for shallow subsurface flow and water table depth (HSB model) and an infinite slope stability method based on the Mohr-Coulomb failure law. The resulting hillslope-storage Boussinesq stability model (HSB-SM) is able to simulate rain-induced shallow landsliding on hillslopes with non-constant bedrock slope and non-parallel plan shape. We apply the model to nine characteristic hillslope types with three different profile curvatures (concave, straight, convex) and three different plan shapes (convergent, parallel, divergent). In the presented model, the unsaturated storage has been calculated based on the unit head gradient assumption. To relax this assumption and to investigate the effect of neglecting the variations of unsaturated storage on the assessment of slope stability in the transient case, we also combine a coupled model of saturated and unsaturated storage and the infinite slope stability method. The results show that the variations of the unsaturated zone storage do not play a critical role in hillslope stability. Therefore, it can be concluded that the presented dynamic slope stability model (HSB-SM) can be used safely for slope stability analysis on complex hillslopes. Our results show that after a certain period of rainfall the convergent hillslopes with concave and straight profiles become unstable more quickly than others, whilst divergent convex hillslopes remain stable (even after intense rainfall). In addition, the relation between subsurface flow and hillslope stability has been investigated. Our analyses show that the minimum safety factor (FS) occurs when the rate of subsurface flow is a maximum. In fact, by increasing the subsurface flow, stability decreases for all hillslope shapes
Application of a probabilistic model of rainfall-induced shallow landslides to complex hollows
Talebi, A. ; Uijlenhoet, R. ; Troch, P.A. - \ 2008
Natural Hazards and Earth System Sciences 8 (2008)4. - ISSN 1561-8633 - p. 733 - 744.
storage boussinesq model - physically-based model - slope stability model - hydrologic response - hillslope stability - subsurface flow - soil production - steep - catchment - valley
Recently, D'Odorico and Fagherazzi (2003) proposed "A probabilistic model of rainfall-triggered shallow landslides in hollows" (Water Resour. Res., 39, 2003). Their model describes the long-term evolution of colluvial deposits through a probabilistic soil mass balance at a point. Further building blocks of the model are: an infinite-slope stability analysis; a steady-state kinematic wave model (KW) of hollow groundwater hydrology; and a statistical model relating intensity, duration, and frequency of extreme precipitation. Here we extend the work of D'Odorico and Fagherazzi (2003) by incorporating a more realistic description of hollow hydrology (hillslope storage Boussinesq model, HSB) such that this model can also be applied to more gentle slopes and hollows with different plan shapes. We show that results obtained using the KW and HSB models are significantly different as in the KW model the diffusion term is ignored. We generalize our results by examining the stability of several hollow types with different plan shapes (different convergence degree). For each hollow type, the minimum value of the landslide-triggering saturated depth corresponding to the triggering precipitation (critical recharge rate) is computed for steep and gentle hollows. Long term analysis of shallow landslides by the presented model illustrates that all hollows show a quite different behavior from the stability view point. In hollows with more convergence, landslide occurrence is limited by the supply of deposits (supply limited regime) or rainfall events (event limited regime) while hollows with low convergence degree are unconditionally stable regardless of the soil thickness or rainfall intensity. Overall, our results show that in addition to the effect of slope angle, plan shape (convergence degree) also controls the subsurface flow and this process affects the probability distribution of landslide occurrence in different hollows. Finally, we conclude that incorporating a more realistic description of hollow hydrology (instead of the KW model) in landslide probability models is necessary, especially for hollows with high convergence degree which are more susceptible to landsliding
A steady-state analytical slope stability model for complex hillslopes
Talebi, A. ; Troch, P.A. ; Uijlenhoet, R. - \ 2008
Hydrological Processes 22 (2008)4. - ISSN 0885-6087 - p. 546 - 553.
storage boussinesq model - physically-based model - subsurface flow - scale
This paper presents a steady-state analytical hillslope stability model to study the role of topography on rain-induced shallow landslides. We combine a bivariate continuous function of the topographic surface, a steady-state hydrological model of hillslope saturated storage, and the infinite slope stability assumption to investigate the interplay between terrain characteristics, saturated storage within hillslopes and soil mechanics. We demonstrate the model by examining 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). For each hillslope type, the steady-state saturated storage corresponding to given recharge rates is computed for three different average bedrock slope angles. On the basis of the infinite slope stability method, the factor of safety (FS) along the hillslopes is determined. Our results demonstrate that in the steep slopes, the least stable situation occurs in hillslopes with convergent plan shapes and concave length profiles, while the convex ones are more stable. In addition to testing our method 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 pre-defined 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. However, we find that the effect of plan shape is more pronounced for convex length profiles. Overall, 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.
Curvature distribution within hillslopes and catchments and its effect on the hydrological response
Bogaart, P.W. ; Troch, P.A.A. - \ 2006
Hydrology and Earth System Sciences 10 (2006)6. - ISSN 1027-5606 - p. 925 - 936.
digital elevation models - drainage-basin evolution - landscape morphology - similarity approach - subsurface flow - saturation - topmodel - prediction - transport - density
Topographic convergence and divergence are first order controls on the hillslope and catchment hydrological response, as evidenced by similarity parameter analyses. Hydrological models often do not take convergence as measured by contour curvature directly into account; instead they use comparable measures like the topographic index, or the hillslope width function. This paper focuses on the question how hillslope width functions and contour curvature are related within the Plynlimon catchments, Wales. It is shown that the total width function of all hillslopes combined suggest that the catchments are divergent in overall shape, which is in contrast to the perception that catchments should be overall convergent. This so-called convergence paradox is explained by the effect of skewed curvature distributions and extreme curvatures near the channel network. The hillslope-storage Bossiness (hsB) model is used to asses the effect of within-hillslope convergence variability on the hydrological response. It is concluded that this effect is small, even when the soil saturation threshold is exceeded. Also described in this paper is a novel algorithm to compute flow path lengths on hillslopes towards the drainage network, using the multi-directional flow redistribution method
Storage-dependent drainable porosity for complex hillslopes
Hilberts, A.G.J. ; Troch, P.A.A. ; Paniconi, C. - \ 2005
Water Resources Research 41 (2005)6. - ISSN 0043-1397 - p. W06001 - W06001.
free-surface flow - time-varying recharge - variable source areas - aquifer-test data - capillarity correction - boussinesq model - subsurface flow - unconfined-aquifer - soil-moisture - groundwater
In hydraulic groundwater theory the parameter drainable porosity f (a storage coefficient that accounts for the effect of the unsaturated zone on water table dynamics) is usually treated as a constant. For shallow unconfined aquifers the value of this parameter, however, depends on the depth to the water table and the water retention characteristics of the soil. In this study an analytical expression for f as a function of water table depth is derived under the assumption of quasi-steady state hydraulic equilibrium, in this way accounting, in part, for the effects of the unsaturated zone on groundwater dynamics. The derived expression is implemented in the nonlinear hillslope-storage Boussinesq (HSB) model (Troch et al., 2003) to simulate the drainage response of complex hillslopes. The model's behavior is analyzed by comparison to (1) the HSB model with a constant value for f and (2) measurements of water tables and outflow hydrographs on a 6.0 × 2.5 × 0.5 m laboratory hillslope experiment. The comparison is conducted for a pure drainage case on two different hillslope shapes (linearly convergent and divergent) and for three different slope inclinations (5%, 10%, and 15%). Comparison 1 is run in an uncalibrated and a fully calibrated mode, and it enables us to evaluate the effect of a dynamic, state-dependent value for f on model output. Comparison 2 allows us to test the HSB model on several hillslope configurations and to analyze whether the concept of a storage-dependent f enhances the model performance. The comparison of the HSB models to the measurements from the laboratory hillslopes shows that it is possible to capture the general features of the outflow hydrograph during a drainage experiment using either one of the HSB models. Overall, the original (constant f) HSB model, with one fitting parameter more than the revised HSB model, shows a slightly better fit on the hydrographs when compared to the revised (variable f) HSB model. However, the peak outflow values (the first few minutes after initiation of the experiments) are better captured by the revised HSB model. The revised HSB model's performance in simulating water table movements is much more accurate than that of the original HSB model. The improved match of the revised HSB model to piezometric measurements is worth stressing because the ability to model water tables is a key attribute of the model, making it possible to investigate phenomena such as saturation excess runoff. Also noteworthy is the good match between the revised HSB model and the outflow measurements, without any calibration, for the divergent slopes. The changing values of the calibrated drainable porosity parameter for the original HSB model as different configurations are simulated (slope angle, plan shape, initial conditions), together with the ability of the revised HSB model to more accurately simulate water table dynamics, clearly demonstrates the importance of regarding drainable porosity as a dynamic, storage-dependent parameter
Analytical solution of the linearized hillslope-storage Boussinesq equation for exponential hillslope width functions
Troch, P.A.A. ; Loon, A.H. van; Hilberts, A.G.J. - \ 2004
Water Resources Research 40 (2004). - ISSN 0043-1397 - p. W08601 - W08601.
regen - oppervlakkige afvoer - grondwaterstroming - modellen - infiltratie - hydrologie van stroomgebieden - hellingen - rain - runoff - groundwater flow - models - infiltration - catchment hydrology - slopes - variable source areas - subsurface flow - complex hillslopes - model
This technical note presents an analytical solution to the linearized hillslope-storage Boussinesq equation for subsurface flow along complex hillslopes with exponential width functions and discusses the application of analytical solutions to storage-based subsurface flow equations in catchment studies.
The hillslope-storage Boussinesq model for non-constant bedrock slope
Hilberts, A.G.J. ; Loon, E.E. van; Troch, P.A.A. ; Paniconi, C. - \ 2004
Journal of Hydrology 291 (2004)3-4. - ISSN 0022-1694 - p. 160 - 173.
generating surface runoff - variable source areas - subsurface flow - complex hillslopes - overland-flow - soil-moisture - equation - stormflow - drainage - richards
In this study the recently introduced hill slope-storage Boussinesq (hsB) model is cast in a generalized formulation enabling the model to handle non-constant bedrock slopes (i.e. bedrock profile curvature). This generalization extends the analysis of hydrological behavior to hillslopes of arbitrary geometrical shape, including hillslopes having curved profile shapes. The generalized hsB model performance for a free drainage scenario is evaluated by comparison to a full three-dimensional Richards equation (RE) based model. The rnodel results are presented in the form of dimensionless storage profiles and dimensionless outflow hydrographs. In addition, comparison of both models to a storage based kinematic wave (KW) model enables us to assess the relative importance of diffusion processes for different hillslope shapes, and to analyze the influence of profile curvature on storage and flow patterns specifically. The comparison setup consists of a set of nine gentle (5% bedrock slope) and nine steep (30% bedrock slope) hillslopes of varying plan shape and profile curvature. Interpretation of the results shows that for highly conductive soils the simulated storage profiles and outflow hydrographs of the generalized hsB model and RE model match remarkably for 5% bedrock slope and for all plan and profile curvatures. The match is slightly poorer on average for 30% bedrock slope, in particular, on divergently shaped hillslopes. In the assessment of the influence of hydraulic diffusion, we find good agreement in Simulation results for the KW model compared to results from the generalized hsB model and the RE model for steep divergent and uniform hillslopes, due to a relatively low ratio between water table gradient and bedrock slope compared to convergent or gentle hillslopes. Overall, we demonstrate that, in addition to bedrock slope, hillslope shape as represented by plan and profile curvature is an important control on subsurface flow response. (C) 2004 Elsevier B.V. All rights reserved.