a steady state analytical slope stability model for complex hillslopes 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

hillslope storage boussinesq model for subsurface flow and variable source areas along complex hillslopes 2 intercomparison with a three dimensional richards equation model 1 the boussinesq equation for subsurface flow in an idealized sloping aquifer of unit width has recently been extended to hillslopes of arbitrary geometry by incorporating the hillslope width function w x into the governing equation where x is the flow distance along the length of the hillslope troch et al 2003 introduction of a source sink term n allows simulation of storm interstorm sequences in addition to drainage processes while a function sc x representing the maximum subsurface water storage can be used to account for surface saturation response in variable source areas activated by the saturation excess mechanism of runoff generation the model can thus simulate subsurface flow and storage dynamics for nonidealized more realistic hillslope configurations in this paper we assess the behavior of this relatively simple one dimensional model in a series of intercomparison tests with a fully three dimensional richards equation model special attention is given to the discretization and setup of the boundary and initial conditions for seven representative hillslopes of uniform convergent and divergent plan shape drainage and recharge experiments are conducted on these hillslopes for both gentle 5 and steep 30 bedrock slope angles the treatment and influence of the drainable porosity parameter are also considered and for the uniform idealized hillslope case the impact of the unsaturated zone is examined by running simulations for different capillary fringe heights in general terms the intercomparison results show that the hillslope storage boussinesq model is able to capture the broad shapes of the storage and outflow profiles for all of the hillslope configurations in specific terms agreement with the richards equation results varies according to the scenario being simulated the best matches in outflow hydrographs were obtained for the drainage experiments suggesting a greater influence of the unsaturated zone under recharge conditions due to transmission of water throughout the hillslope in the spatiotemporal water table response a better match was observed for convergent than divergent hillslopes and the bedrock slope angle was not found to greatly influence the quality of the agreement between the two models on the basis of the intercomparison experiments we make some suggestions for further development and testing of the hillslope storage model

two dimensional soil moisture flow in a sloping rectangular region experimental and numerical studies results from experiments with a 3 66 by 0 58 by 0 108 m flume filled with sand are used to study the two dimensional flow of soil moisture under the condition of rainfall infiltration the experimental results are compared to results obtained by a numerical solution via a finite element finite difference transformation of the two dimensional richards equation the results are presented in the form of flow field conditions hydraulic head distribution and position of the phreatic surface and the rising limb of the runoff hydrograph the experimental and the numerical results are in satisfactory agreement when the effect of capillary hysteresis is incorporated into the numerical solution when capillary hysteresis is ignored the numerically simulated hydrograph lags far behind the experimentally derived hydrograph

modeling subsurface stormflow on steeply sloping forested watersheds five mathematical models for predicting subsurface flow were compared to discharge measurements made by hewlett and hibbert 1963 on a uniform sloping soil trough at the coweeta hydrologic laboratory the models included one and two dimensional finite element models based on the richards equation a kinematic wave model and two simple storage discharge models based on the kinematic wave and boussinesq assumptions the simple models simulated the subsurface response and water table positions as well as the more complex models based on the richards equation and were much more economical to use from the point of view of computational costs such models have features that would allow them to be incorporated into more complex watershed models thus placing hydrologic prediction on a more physically correct and less empirical footing

analytical solutions to hillslope subsurface storm flow and saturation overland flow we present the analytical solutions to a hillslope based formulation of subsurface storm flow and saturation overland flow here a hillslope is defined as the area between two streamlines originating from two ends of a channel link or from the channel head and ending at the ridgelines the three dimensional soil mantle of a hillslope is reduced to a one dimensional profile along which the soil moisture and discharge are modeled continuity and a kinematic form of darcy s law lead to quasi linear wave equations solvable with the method of characteristics examples are given to illustrate the ability and limitations of the solutions in capturing the essential runoff behavior of different slope types

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

a two state integral balance model for soil moisture and groundwater dynamics in complex terrain a dynamical model is devised for a hydrologic system where unsaturated and saturated storage serve as the principal control on rainfall runoff and where complex topography drainage area and variable depth of moisture penetration describe the flow geometry the model is formed by direct integration of the local conservation equation with respect to the partial volumes occupied by unsaturated and saturated moisture storage respectively this yields an integral balance model in just two state variables the relationship of the dynamical model to field data in complex terrain is found through a joint probability density for terrain features this serves as a volume weighting function to construct conditional averages for the state variables and fluxes over a specified range of terrain features the scale of averaging could range from hillslopes to river basins two examples of the joint probability of terrain features altitude and aspect are demonstrated for valley ridge and appalachian plateau digital elevation models the strategy of a dynamical model formed by conditional averages of state variables with respect to terrain features is proposed as a way of simplifying the dynamics while preserving the natural spatial and temporal scales contributing to runoff response the parametric form of the storage flux or constitutive relationships for the proposed model is determined from numerical experiments in a simple hillslope flow geometry the results show that a competitive relation exists between unsaturated and saturated storage except for the lowest precipitation rates saturation overland flow is proposed to be a storage feedback relation solutions to the integral balance model are presented in terms of the phase portrait which represents all possible solution trajectories in state space the timing and magnitude of peaks in the runoff hydrograph from pulse type input events demonstrate quick flow from near stream saturated storage saturation overland flow including rejected rainfall storage feedback and late time infiltration from upslope subsurface flow

numerical analysis on influence of principal parameters of topography on hillslope instability in a small catchment this study was conducted to identify the influence of three principal parameters constituting topography slope inclination soil depth and slope length on hillslope instability in a small catchment known as higashifukubegawa of shikoku island western japan the typhoon rainfall of 19 20 october 2004 was significant in causing a total of seven slope failures in the catchment though other rainfall events of various intensities in the same year did not cause failure to understand the influence of the three principal parameters numerical modeling of seepage and slope stability was performed in slope profiles constructed by varying the three parameters across their permissible range prepared from the seven slope failures of higashifukubegawa in geostudio geostudio tutorials includes student edition lessons geo slope international ltd calgary 2005 v 4 the change in porewater pressure and slope mass weight due to variation in values of principal parameters was used to interpret the change in factor of safety or instability the results showed that 1 instability increases with increase in the values of all three selected parameters across their range in higashifukubegawa with remarkable decreasing trend in factors of safety 2 slope inclination and soil depth were observed to affect instability through change in both unsaturated zone moisture content and mobilizing force of slope mass 3 but with slope length the unsaturated zone moisture content was not found to change considerably which implies that the instability due to slope length is mainly governed by change in slope mass weight overall this study has dealt in great detail with how hillslope instability changes with principal parameters of topography under the same simulating conditions of hydrological and geo mechanical parameters

hillslope runoff processes and models abstract hillslope hydrology is concerned with the partition of precipitation as it passes through the vegetation and soil between overland flow and subsurface flow flow follows routes which attenuate and delay the flow to different extents so that a knowledge of the relevant mechanisms is important in the 1960s and 1970s hillslope hydrology developed as a distinct topic through the application of new field observations to develop a generation of physically based forecasting models in its short history theory has continually been overturned by field observation thus the current tendency particularly among temperate zone hydrologists to dismiss all hortonian overland flow as a myth is now being corrected by a number of significant field studies which reveal the great range in both climatic and hillslope conditions some recent models have generally attempted to simplify the processes acting for example including only vertical unsaturated flow and lateral saturated flows others explicitly forecast partial or contributing areas with hindsight the most complete and distributed models have generally shown little forecasting advantage over simpler approaches perhaps trending towards reliable models which can run on desk top microcomputers the variety now being recognised in hillslope hydrological responses should also lead to models which take account of more complex interactions even if initially with a less secure physical and mathematical basis than the richards equation in particular there is a need to respond to the variety of climatic responses and to spatial variability on and beneath the surface including the role of seepage macropores and pipes which call into question whether the hillside can be treated as a darcian flow system

storage dependent drainable porosity for complex hillslopes 1 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

a new equation for shallow groundwater flow over a curved impermeable boundary numerical solutions and laboratory tests 1 the flow of recharge induced shallow groundwater over an impermeable boundary is a basic process in hillslope hydrology which has usually been simplified by taking the boundary as having a constant slope previously published equations in curvilinear coordinates have been reduced here to a single equation for shallow groundwater flow over an impermeable boundary with continuous curvature subject to conditions the equation has been verified by comparison with a finite difference solution of the steady flow case and with a range of experimental data from a viscous flow physical model for both steady and transient flows the results show that while the bed profile affects flow depths it has relatively little impact on the outflow hydrograph it was found that the outflow is closely approximated by a power relationship with the volume in storage and this leads to a simple algorithm for predicting the outflow hydrograph under conditions of variable recharge

remains of the day preservation of organic micro residues on stone tools here i report on the decay processes of microscopic organic residues left on stone tool surfaces after their use residue analysis on ancient stone tools facilitates reconstruction of past activities this study enables predictions about the circumstances under which ancient residues preserve experimental tool sets with modern residues were buried for a year in separate deposits at sterkfontein sibudu south africa and zelhem the netherlands whose ph and geomorphology varied they were then analysed using light microscopy biological weathering mainly causes residue decay in unstable environments rich in microbes and micro organisms residues decay quickly from an archaeological perspective this means that sites that are stable desiccated waterlogged extremely acidic or alkaline and extremely cold or hot sites different residue types have different preservation optima and this may lead to a preservation and perhaps interpretation bias the preliminary predictive models presented in this paper could aid in the considered selection of sites and samples

on the use of the boussinesq equation for interpreting recession hydrographs from sloping aquifers 1 the method of recession analysis proposed by brutsaert and nieber 1977 remains one of the few analytical tools for estimating aquifer hydraulic parameters at the field scale and beyond in the method the recession hydrograph is examined as dq dt f q where q is aquifer discharge and f is an arbitrary function the observed function f is parameterized through analytical solutions to the one dimensional boussinesq equation for unconfined flow in a homogeneous and horizontal aquifer while attractive in its simplicity as originally presented it is not applicable to settings where slope is an important driver of flow or where hydraulic parameters vary greatly with depth we compare analytical solutions to the linearized one dimensional boussinesq equation for a sloping aquifer to numerical solutions of the full nonlinear equation the behavior of the nonlinear boussinesq equation is also assessed when the aquifer is heterogeneous wherein the lateral saturated hydraulic conductivity k varies as a power law with height z above the impermeable layer k zn n constant 0 all of the analytical solutions differ in key aspects from the nonlinear solution when plotted as dq dt f q and thus are inappropriate for a brutsaert and nieber type analysis however new analytical solutions for a sloping aquifer are derived empirically from the numerical simulations that are applicable during the late period of recession when the recession curve converges to dq dt aqb where b 2n 1 n 1 and a is a function of the dimensions and hydraulic properties of the aquifer

analytical solution of the linearized hillslope storage boussinesq equation for exponential hillslope width functions 1 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 importance of hydraulic groundwater theory in catchment hydrology the legacy of wilfried brutsaert and jean yves parlange based on a literature overview this paper summarizes the impact and legacy of the contributions of wilfried brutsaert and jean yves parlange cornell university with respect to the current state of the art understanding in hydraulic groundwater theory forming the basis of many applications in catchment hydrology ranging from drought flow analysis to surface water groundwater interactions hydraulic groundwater theory simplifies the description of water flow in unconfined riparian and perched aquifers through assumptions attributed to dupuit and forchheimer boussinesq 1877 derived a general equation to study flow dynamics of unconfined aquifers in uniformly sloping hillslopes resulting in a remarkably accurate and applicable family of results though often challenging to solve due to its nonlinear form under certain conditions the boussinesq equation can be solved analytically allowing compact representation of soil and geomorphological controls on unconfined aquifer storage and release dynamics the boussinesq equation has been extended to account for flow divergence convergence as well as for nonuniform bedrock slope concave convex the extended boussinesq equation has been favorably compared to numerical solutions of the three dimensional richards equation confirming its validity under certain geometric conditions analytical solutions of the linearized original and extended boussinesq equations led to the formulation of similarity indices for baseflow recession analysis including scaling rules to predict the moments of baseflow response validation of theoretical recession parameters on real world streamflow data is complicated due to limited measurement accuracy changing boundary conditions and the strong coupling between the saturated aquifer with the overlying unsaturated zone however recent advances are shown to have mitigated several of these issues the extended boussinesq equation has been successfully applied to represent baseflow dynamics in catchment scale hydrological models and it is currently considered to represent lateral redistribution of groundwater in land surface schemes applied in global circulation models from the review it is clear that wilfried brutsaert and jean yves parlange stimulated a body of research that has led to several fundamental discoveries and practical applications with important contributions in hydrological modeling

kinematic subsurface stormflow this paper builds on the analysis of henderson and wooding 1964 in comparing simplified models of subsurface stormflow for the case of a sloping soil mantle in which the hydraulic conductivity is constant throughout it is shown that models based on a kinematic wave formulation may be good approximations for those based on the extended dupuit forchheimier assumptions for values of the nondimensional parameter 4i cos k sin2 less than about 0 75 in terms of predicting both water table profiles and subsurface stormflow hydrographs by using this critical value of the range of values of slope angle and saturated hydraulic conductivity for which the kinematic approximation is valid can be specified a comparison is made with slope angles and hydraulic conductivities at field sites where subsurface stormflow has been shown to be an important component of catchment storm response it is concluded that the kinematic approximation may be useful for cases of practical interest

improved calibration procedures and new standards for u pb and th pb dating of phanerozoic xenotime by ion microprobe abstract xenotime is a widely occurring mineral that is amenable to u pb and th pb dating but often is found as micrometre sized crystals that can only be dated by in situ microanalytical techniques determining accurate ages for phanerozoic samples and assessing concordance in older samples requires accurate determination of pb u and pb th however ion microprobe data for these ratios are affected by the highly variable trace element composition of xenotime we have identified calibration procedures including matrix corrections for the effects of the dominant trace elements u th and ree that provide an accuracy of 1 for pb u and

saturated area formation on nonconvergent hillslope topography with shallow soils a numerical investigation prediction of saturated area formation is important for hydrologic modeling of watersheds with shallow highly pervious soils this simulation study examines the relative importance of hillslope properties and rainfall rate on the evolution of saturated source areas during wetting the study focuses on homogeneous nonconvergent hillslope topography with constant slope the two dimensional variably saturated groundwater model vs2d healy 1990 lappala et al 1993 is used to simulate saturated area formation under the action of steady uniform rainfall the study methodology systematically varies four hillslope properties depth to impervious layer slope length slope angle and average saturated hydraulic conductivity and the rainfall rate results indicate that the fraction of the hillslope length that is saturated at equilibrium is a function of a parameter which is defined as the rainfall rate multiplied by the slope length divided by the slope angle soil thickness and saturated hydraulic conductivity the temporal evolution of saturated area is analyzed in terms of the equilibrium time nonlinearity in the unsaturated zone and differences in hillslope properties result in a nonunique time to equilibrium relation the time to equilibrium is maximum when factors that tend to cause surface saturation are in approximate balance with those that tend to dissipate surface saturation the temporal evolution of surface saturation during wetting follows a wide variety of trajectories equivalent hillslope soil water storage ratios on slopes with different properties can result in a wide range of surface saturation conditions hillslopes with shallower soils and smaller slope angles are most susceptible to saturated area formation however sudden changes in surface saturation are possible on steep hillslopes when 1 6

some analytical solutions of the linearized boussinesq equation with recharge for a sloping aquifer subsurface flow from a hillslope can be described by the hydraulic groundwater theory as formulated by the boussinesq equation several attempts have been made to solve this partial differential equation and exact solutions have been found for specific situations in the case of a sloping aquifer brutsaert 1994 suggested linearizing the equation to calculate the unit response of the hillslope in this paper we first apply the work of brutsaert by assuming a constant recharge to the groundwater table the solution describes the groundwater table levels and the outflow in function of time then an analytical expression is derived for the steady state solution by allowing time to approach infinity this steady state water table is used as an initial condition to derive another analytical solution of the boussinesq equation this can then be used in a quasi steady state approach to compute outflow under changing recharge conditions subsurface flow from a hillslope can be described by the hydraulic groundwater theory as formulated by the boussinesq equation several attempts have been made to solve this partial differential equation and exact solutions have been found for specific situations in the case of a sloping aquifer brutsaert 1994 suggested linearizing the equation to calculate the unit response of the hillslope in this paper we first apply the work of brutsaert by assuming a constant recharge to the groundwater table the solution describes the groundwater table levels and the outflow in function of time then an analytical expression is derived for the steady state solution by allowing time to approach infinity this steady state water table is used as an initial condition to derive another analytical solution of the boussinesq equation this can then be used in a quasi steady state approach to compute outflow under changing recharge conditions

a hybrid 3d hillslope hydrological model for use in earth system models hillslope scale rainfall runoff processes leading to a fast catchment response are not explicitly included in land surface models lsms for use in earth system models esms due to computational constraints this study presents a hybrid 3d hillslope hydrological model h3d that couples a 1 d vertical soil column model with a lateral pseudo 2d saturated zone and overland flow model for use in esms by representing vertical and lateral responses separately at different spatial resolutions h3d is computationally efficient the h3d model was first tested for three different hillslope planforms uniform convergent and divergent we then compared h3d with single and multiple soil columns with a complex physically based 3 d model and a simple 1 d soil moisture model coupled with an unconfined aquifer as typically used in lsms it is found that simulations obtained by the simple 1 d model vary considerably from the complex 3 d model and are not able to represent hillslope scale variations in the lateral flow response in contrast the single soil column h3d model shows a much better performance and saves computational time by 2 3 orders of magnitude compared with the complex 3 d model when multiple vertical soil columns are implemented the resulting hydrological responses soil moisture water table depth and base flow along the hillslope from h3d are nearly identical to those predicted by the complex 3 d model but still saves computational time as such the computational efficiency of the h3d model provides a valuable and promising approach to incorporating hillslope scale hydrological processes into continental and global scale esms

partial resetting of u pb ages during experimental fluid induced re equilibration of xenotime abstract experimentally metasomatized xenotime was investigated in terms of preservation of u pb ages during fluid induced alterations at 250 450 550 and 650 c starting materials for experiments included xenotime 38 4 0 6 ma albite k feldspar biotite muscovite garnet sio2 caf2 na2si2o5 and h2o that roughly replicated metapelitic to granitic composition with high na ca si and f activities in the fluid despite partial replacement of xenotime by secondary phases including y ree rich fluorapatite to y rich fluorcalciobritholite in all runs and an unnamed y hree rich silicate in 250 c experiment only two experiments at 550 c 800 mpa and 650 c 600 mpa resulted in development of faint to moderate patchy zoning in the xenotime experimental results indicate higher chemical stability of xenotime at lower p t conditions compared to those corresponding to amphibolite facies conditions the xenotime domains metasomatized via coupled dissolution reprecipitation reactions are characterized by depletion of u and pb and younger 206pb 238u dates of ca 15 34 ma demonstrating preferential removal of pb and thus the partial resetting of the age record the u pb data for the first time experimentally confirm that xenotime may be affected by re equilibration induced by fluid or melt with high na ca and f activities via coupled dissolution reprecipitation reactions that result in removal of radiogenic pb under temperature conditions of 550 650 c these findings have important implications for u pb geochronology of igneous particularly in pegmatites and metamorphic processes in terms of preservation of u pb ages of xenotime that was affected by multiple thermal events in the presence of alkali rich fluid and or melt

testing the hybrid 3 d hillslope hydrological model in a controlled environment hillslopes are important for converting rainfall into runoff influencing the terrestrial dynamics of the earth s climate system recently we developed a hybrid 3 d h3d hillslope hydrological model that gives similar results as a full 3 d hydrological model but is up to 2 3 orders of magnitude faster computationally here h3d is assessed using a number of recharge drainage experiments within the landscape evolution observatory leo with accurate and high resolution both temporally and spatially observations of the inputs outputs and storage dynamics of several hillslopes such detailed measurements are generally not available for real world hillslopes results show that the h3d model captures the observed storage base flow and overland flow dynamics of both the larger leo and the smaller minileo hillslopes very well sensitivity tests are also performed to understand h3ds difficulty in representing the height of the saturated zone close to the seepage face of the minileo hillslope results reveal that a temporally constant parameters set is able to simulate the response of the minileo for each individual event however when one focuses on the saturated zone dynamics at 0 15 m from the seepage face a stepwise evolution of the optimal model parameter for the saturated lateral conductivity parameter of the gravel layer occurs this evolution might be related to the migration of soil particles within the hillslope however it is currently unclear whether and where this takes place in the seepage face or within the parts of the loamy sand soil

influence of slope on subsurface drainage of hillsides hillside drainage was investigated using numerical solutions to the two dimensional form of the richards equation for combined unsaturated and saturated flow the objectives of the study were to examine the influence of slope on drain flow rates and water table depths in the center regions of sloping hillsides solutions were obtained for slopes 135 m long containing parallel drains spaced 30 m apart and located l m below the surface in 3 and 7 m deep profiles drainage under steady infiltration and for transient conditions was simulated on slopes of up to 0 40 m m using two soils small slopes 0 15 m m were found to have little effect on drain flow rates and water table depths in the center of the region indicating that drainage theory developed for flat land can be used for interior parallel drains on these slopes

a low dimensional physically based model of hydrologic control of shallow landsliding on complex hillslopes 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 copyright 2008 john wiley sons ltd

the hillslope storage boussinesq model for non constant bedrock slope in this study the recently introduced hillslope 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 model 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

hillslope storage boussinesq model for subsurface flow and variable source areas along complex hillslopes 1 formulation and characteristic response 1 hillslope response to rainfall remains one of the central problems of catchment hydrology flow processes in a one dimensional sloping aquifer can be described by boussinesq s hydraulic groundwater theory most hillslopes however have complex three dimensional shapes that are characterized by their plan shape profile curvature of surface and bedrock and the soil depth field studies and numerical simulation have shown that these attributes are the most significant topographic controls on subsurface flow and saturation along hillslopes in this paper the boussinesq equation is reformulated in terms of soil water storage rather than water table height the continuity and darcy equations formulated in terms of storage along the hillslope lead to the hillslope storage boussinesq hsb equation for subsurface flow solutions of the hsb equation account explicitly for plan shape of the hillslope by introducing the hillslope width function and for profile curvature through the bedrock slope angle and the hillslope soil depth function we investigate the behavior of the hsb model for different hillslope types uniform convergent and divergent and different slope angles under free drainage conditions after partial initial saturation drainage scenario and under constant rainfall recharge conditions recharge scenario the hsb equation is solved by means of numerical integration of the partial differential equation we find that convergent hillslopes drain much more slowly compared to divergent hillslopes the accumulation of moisture storage near the outlet of convergent hillslopes results in bell shaped hydrographs in contrast the fast draining divergent hillslopes produce highly peaked hydrographs in order to investigate the relative importance of the different terms in the hsb equation several simplified nonlinear and linearized versions are derived for instance by recognizing that the width function of a hillslope generally shows smooth transition along the flow direction or by introducing a fitting parameter to account for average storage along the hillslope the dynamic response of these reduced versions of the hsb equation under free drainage conditions depend strongly on hillslope shape and bedrock slope angle for flat slopes of the order of 5 only the simplified nonlinear hsb equation is able to capture the dynamics of subsurface flow along complex hillslopes in contrast for steep slopes of the order of 30 we see that all the reduced versions show very similar results compared to the full version it can be concluded that the complex derivative terms of width with respect to flow distance play a less dominant role with increasing slope angle comparison with the hillslope storage kinematic wave model of troch et al 2002 shows that the diffusive drainage terms of the hsb model become less important for the fast draining divergent hillslopes these results have important implications for the use of simplified versions of the hsb equation in landscapes and for the development of appropriate analytical solutions for subsurface flow along complex hillslopes

analytical approximations of discharge recessions for steeply sloping aquifers in alpine catchments the validity and applicability of various methods to infer hydraulic properties of sloping aquifers in alpine settings using the power law relationship between the discharge recession and its first time derivative is explored for this purpose a synthetic spring catchment implemented in the numerical groundwater flow model modflow as well as the example of a relict rock glacier in an alpine setting is examined the various approaches are found to differ particularly in the late time domain whereas most of them agree fairly well in the early time domain and at the transition point between the two time domains as the early recession may be affected by uncertainties from inappropriate initial conditions it is proposed to use the transition point for estimating aquifer thickness and transmissivity using only prolonged winter recessions in the analysis of the field data from the relict rock glacier yields estimates of aquifer thickness and hydraulic conductivity consistent with results from a geophysical survey and tracer tests respectively in the other seasons the recession is frequently interrupted by minor recharge events and using the lower envelope of the entire data is found to yield estimates that are too high in the given case it is thus recommended to focus on the winter recession in the analysis of hydrograph data from alpine settings

understanding geologic processes with xenotime composition chronology and a protocol for electron probe microanalysis abstract xenotime ypo 4 is iso structural with zircon group minerals and lies at one end of a compositional solid solution with monazite as with monazite and zircon naturally occurring xenotime may accommodate significant concentrations of rare earth elements as well as th and u making it an important repository for these valuable geochemical marker elements and a potential geochronometer xenotime grows in sediments during diagenesis in low to granulite grade metamorphic rocks in migmatites and is common in peraluminous igneous rocks xenotime can be a complement or indeed an alternative to monazite and or zircon in geochemical and geochronological studies to maximise the petrographic potential of xenotime a complete understanding of its composition and relationship to rock forming assemblages is essential electron beam techniques provide micron scale resolution of compositional and textural variation and yield precise dates for individual micro volumes in multi domain grains methods for collecting trace element data by electron probe microanalysis differ from those routinely employed to collect major element concentrations careful characterisation of background curvature and background interferences around the th u and pb peaks is required to avoid large overlap correction for y l 2 3 on pb m analysis of pb is made on the m peak a broad array of geochemical and geochronological applications can take advantage of the links between xenotime composition and texture and the evolution of silicate mineral assemblages in a diversity of environments one example of metasomatised xenotime from a pegmatite in sw norway demonstrates a practical application to dating geologic processes as well as the potential limitations that arise in compositionally heterogeneous xenotime

estimation of aquifer lower layer hydraulic conductivity values through base flow hydrograph rising limb analysis 1 the estimation of catchment averaged aquifer hydraulic conductivity values is usually performed through a base flow recession analysis relationships between the first time derivatives of the base flow and the base flow values themselves derived for small and large values of time are used for this purpose however in the derivation of the short time equations an initially fully saturated aquifer without recharge with sudden drawdown is assumed which occurs very rarely in reality it is demonstrated that this approach leads to a nonnegligible error in the parameter estimates a new relationship is derived valid for the rising limb of a base flow hydrograph succeeding a long rainless period application of this equation leads to accurate estimates of the aquifer lower layer saturated hydraulic conductivity further it has been shown analytically that if base flow is modeled using the linearized boussinesq equation the base flow depends on the effective aquifer depth and the ratio of the saturated hydraulic conductivity to the drainable porosity not on these three parameters separately the results of the new short time expression are consistent with this finding as opposed to the use of a traditional base flow recession analysis when base flow is modeled using the nonlinear boussinesq equation the new expression can be used without a second equation for large values of time to estimate the aquifer lower layer hydraulic conductivity overall the results in this paper suggest that the new methodology outperforms a traditional recession analysis for the estimation of catchment averaged aquifer hydraulic conductivities

a base flow separation algorithm based on the linearized boussinesq equation for complex hillslopes 1 the separation of base flow from discharge records is an important issue in hydrology the objective of this paper is to develop a base flow separation algorithm based on groundwater theory in which the shape of the aquifer is taken into account and for which the parameters can be estimated from river discharge measurements for this purpose an analytical solution to the linearized boussinesq equation for realistic aquifer shapes and temporally variable recharge rates is derived this solution is combined with a mass balance at the land surface in order to construct the base flow separation algorithm the parameters of the base flow filter are calculated on the basis of the same analytical solution comparison of the results of the new algorithm to existing base flow separation methods shows the need for a physical basis for base flow filters

low dimensional modeling of hillslope subsurface flow relationship between rainfall recharge and unsaturated storage dynamics 1 we present a coupling between the one dimensional richards equation for vertical unsaturated flow and the one dimensional hillslope storage boussinesq equation hsb for lateral saturated flow along complex hillslopes here the capillary fringe is included in the flow domain as an integral part of the boussinesq aquifer the coupling allows quantitative investigation of the role of unsaturated storage in the relationship between rainfall and recharge the coupled model hsb coupled is compared to the original hsb model hsb original and a three dimensional richards equation re based model taken to be the benchmark on a set of seven synthetic hillslopes ranging from convergent to divergent using hsb original the water tables are overestimated and the outflow rates are generally underestimated and there is no delay between rainfall and recharge the coupled model however shows a remarkably good match with the re model in terms of outflow rates and the delay between rainfall and recharge is captured well we also see a clear improvement in the match to the water tables even though the values are still overestimated for some hillslope shapes in particular the convergent slopes we show that for the hillslope configurations and scenarios examined in this paper it is possible to reproduce hydrographs and water table dynamics with a good degree of accuracy using a low dimensional hydrological model

similarity analysis of subsurface flow response of hillslopes with complex geometry the matter of the efficient and parsimonious parameterization of hillslope subsurface flow remains an important issue in catchment hydrological studies brutsaert 1995 insights into the influence of the shape and hydraulic characteristics of hillslopes is required to further our understanding and our ability to model catchment hydrological processes recently troch et al 2003 introduced the hillslope storage boussinesq hsb equation to describe subsurface flow and saturation along geometrically complex hillslopes the hsb equation can be linearized and further reduced to an advection diffusion equation for subsurface flow in hillslopes with constant bedrock slopes and exponential width functions this paper presents a dimensional analysis of the latter equation in order to study the moments of the characteristic response function crf corresponding to the free drainage of this type of hillslope these moments in a dimensionless form can be expressed as functions of a similarity parameter hereafter called the hillslope peclet number and a group of dimensionless numbers accounting for the effects of the boundary and initial conditions the analytical expressions for the first four central crf moments are derived for two types of initial conditions the analysis of their respective influences shows that the hillslope peclet number is an efficient similarity parameter to describe the hillslope subsurface flow response moreover comparison between the crf moments predicted by means of our similarity analysis and empirical moments derived from outflow measurements for different types of laboratory hillslopes shows good agreement