Lumped hysteretic model for subsurface stormflow developed using downward approach

The terms ‘downward’ and ‘upward’ (synonymous with ‘top‐down’ and ‘bottom‐up’ respectively) are sometimes used when describing methods for developing hydrological models. A downward approach is used here to develop a lumped catchment‐scale model for subsurface stormflow at the 0·94 km² Slapton Wood catchment. During the development, as few assumptions as possible are made about the behaviour of subsurface stormflow at the catchment scale, and no assumptions are made about its behaviour at smaller scales. (In an upward approach, in contrast, the modelling would be based on assumptions about, and data for, the behaviour at smaller scales, such as the hillslope, plot, and point scales.) The model has a single store with a relatively simple relationship between discharge and storage, based on equations describing hysteretic patterns seen in a graph of discharge against storage. Double‐peaked hydrographs have been observed at the catchment outlet. Rainfall on the channel and infiltration‐excess and saturation‐excess runoff give a rapid response, and shallow subsurface stormflow gives a delayed response. Hydrographs are successfully simulated for the large delayed responses observed in 1971–1980 and 1989–1991, then a lumped model for the rapid response is coupled to the lumped hysteretic model and some double‐peaked hydrographs simulated. A physical interpretation is developed for the lumped hysteretic model, making use of information on patterns of perched saturation observed in 1982 on a hillslope at the Slapton Wood catchment. Downward and upward approaches are complementary, and the most robust way to develop and improve lumped catchment models is to iterate between downward and upward steps. Possible next steps are described. Copyright © 2006 John Wiley & Sons, Ltd.     

Stability and accuracy of two-dimensional kinematic wave overland flow modeling

A two-dimensional finite element based overland flow model was developed and used to study the accuracy and stability of three numerical schemes and watershed parameter aggregation error. The conventional consistent finite element scheme results in oscillations for certain time step ranges. The lumped and the upwind finite element schemes are tested as alternatives to the consistent scheme. The upwind scheme did not improve on the stability or the accuracy of the solution, while the lumped scheme provided stable and accurate solutions for time steps twice the size of time steps needed for the consistent scheme. A new accuracy based dynamic time step estimate for the two-dimensional overland flow kinematic wave solution is developed for the lumped scheme. The newly developed dynamic time step estimates are functions of the mesh size, and time of concentration of the watershed hydrograph. Due to lack of analytical solutions, the time step was developed by comparing numerical solutions of various levels of discretization to a reference solution using a very fine mesh and a very small time step. The time step criteria were tested on a different set of problems and proved to be adequate for accurate and stable solutions. A sensitivity analysis for the watershed slope, Manning’s roughness coefficient and excess rainfall rate was conducted in order to test the effect of parameter aggregation on the stability and accuracy of the solution. The results of this analysis show that aggregation of the slope data resulted in the highest error. The roughness coefficient had a smaller effect on the solution while the rainfall intensity did not show any significant effect on the flow rate solution for the range of rainfall intensity used. This work pioneers the challenge of providing guidelines for accurate and stable numerical solutions of the two-dimensional kinematic wave equations for overland flow.     

Coupling the Xinanjiang model to a kinematic flow model based on digital drainage networks for flood forecasting

The Xinanjiang model, which is a conceptual rainfall‐runoff model and has been successfully and widely applied in humid and semi‐humid regions in China, is coupled by the physically based kinematic wave method based on a digital drainage network. The kinematic wave Xinanjiang model (KWXAJ) uses topography and land use data to simulate runoff and overland flow routing. For the modelling, the catchment is subdivided into numerous hillslopes and consists of a raster grid of flow vectors that define the water flow directions. The Xinanjiang model simulates the runoff yield in each grid cell, and the kinematic wave approach is then applied to a ranked raster network. The grid‐based rainfall‐runoff model was applied to simulate basin‐scale water discharge from an 805‐km² catchment of the Huaihe River, China. Rainfall and discharge records were available for the years 1984, 1985, 1987, 1998 and 1999. Eight flood events were used to calibrate the model's parameters and three other flood events were used to validate the grid‐based rainfall‐runoff model. A Manning's roughness via a linear flood depth relationship was suggested in this paper for improving flood forecasting. The calibration and validation results show that this model works well. A sensitivity analysis was further performed to evaluate the variation of topography (hillslopes) and land use parameters on catchment discharge. Copyright © 2009 John Wiley & Sons, Ltd.     

Modelling hysteretic behaviour of coupled walls for dynamic analysis

Modelling techniques for dynamic inelastic response analysis of coupled wall structures are investigated. Emphasis is placed on effects of parameters defining the force-displacement hysteresis loop. Specifically, effects of axial force-moment interaction, strength reduction, shear yielding, pinching, reloading and unloading branches of hysteresis loops are considered. Effects of modelling parameters on selected response quantities are investigated and discussed in detail. A 20-storey coupled wall structure was selected for dynamic analysis. Ranges of parameters characterizing force-displacement hysteresis loops were obtained from laboratory tests under slowly reversed static loading. Previously recorded strong motion accelerograms were used as input motions. Results indicate that wall axial forces and beam strength reduction can have significant effects on response envelopes. Moderate variations in unloading and reloading branches of hysteresis loops and pinching appear to have little effect on dynamic response.     

Accuracy of kinematic wave and diffusion wave approximations for time-independent flows

Errors in the kinematic wave and diffusion wave approximations for time-independent (or steady-state) cases of channel flow were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors in the range 1–2% for values of KF (? 7.5), where K is the kinematic wave number and F₀ is the Froude number. Even for small values of KF (e.g. KF²₀ = 0.75), the errors were typically less than 15%. The accuracy of the diffusion wave approximation was greatly influenced by the downstream boundary condition. The error of the kinematic wave approximation was found to be less than 13% in the region 0.1 ? x ? 0.95 for KF = 7.5 and was greater than 30% for smaller values of KF (? 0.75). This error increased with strong downstream boundary control.     

橡胶垫隔震装置的双向弹塑性恢复力模型

改进了铅芯叠层钢板橡胶垫隔震装置的Park模型，提出其双向弹塑性恢复力模型。建议的模型克服了Park模型不能从橡胶垫力学试验曲线上直观获取所需参数的缺点。采用本文建议模型的结构分析程序HBTA2．0可以方便地用于实际隔震结构的弹塑性动力分析，计算结果也更为合理。     

Accuracy of kinematic wave and diffusion wave for spatial‐varying rainfall excess over a plane

The kinematic‐wave and diffusive‐wave approximations were investigated for unsteady overland flow resulting from spatially varying rainfall excess. Three types of boundary conditions were adopted: zero flow at the upstream end, and critical flow and zero depth‐gradient at the downstream end. Errors were derived by comparing the dimensionless profiles of the flow depth over the plane with those computed from the dynamic‐wave solution. It was found that the mean errors for both the approximations were independent of the type of rainfall excess distribution for KF₀² > 5, where K is the kinematic‐wave number and F₀ is the Froude number. Therefore, the regions (KF₀², F₀) where the kinematic‐wave and diffusive‐wave solutions would be fairly accurate and for any distribution of spatially varying rainfall, were characterized. The kinematic‐wave approximation was reasonably accurate, with a mean error of less than 5% and for the critical depth at the downstream end, for KF₀² ≥ 20 with F₀ ≤ 1; if the rainfall excess was concentrated in a portion of the plane, the field where the kinematic‐wave solution was found accurate, it was more limited and characterized for KF₀² > 35 with F₀ ≤ 1. The diffusive‐wave solution was in good agreement with the dynamic‐wave solution with a mean error of less than 5%, in the flow depth, for KF₀² ≥ 15 with F₀ ≤ 1; for rainfall excess concentrated in a portion of the plane, the accuracy of the diffusion wave solution was in a region more restricted and defined for KF₀² ≥ 30 with F₀ ≤ 1. For zero‐depth gradient at the downstream end, the accuracy field of the kinematic‐wave was found to be greater and characterized for KF₀² > 10 with F₀ ≤ 1; for rainfall excess concentrated in a portion of the plane, the region was smaller and defined for KF₀² > 15 with F₀ ≤ 1. The diffusive‐wave solution was found accurate in the region defined for KF₀² > 7·5, whereas for rainfall excess concentrated in a portion of the plane, the field of accuracy was for KF₀² > 12·5 with F₀ ≤ 1. The lower limits of the regions, defined on KF₀², can be considered generally valid for both approximations, but for F₀ < 1 smaller lower limits were also characterized. Finally, the accuracy of these approximations was influenced significantly by the downstream boundary condition. Copyright © 2002 John Wiley & Sons, Ltd.     

Connectivity metrics for subsurface flow and transport

Understanding the role of connectivity for the characterization of heterogeneous porous aquifers or reservoirs is a very active and new field of research. In that framework, connectivity metrics are becoming important tools to describe a reservoir. In this paper, we provide a review of the various metrics that were proposed so far, and we classify them in four main groups. We define first the static connectivity metrics which depend only on the connectivity structure of the parameter fields (hydraulic conductivity or geological facies). By contrast, dynamic connectivity metrics are related to physical processes such as flow or transport. The dynamic metrics depend on the problem configuration and on the specific physics that is considered. Most dynamic connectivity metrics are directly expressed as a function of an upscaled physical parameter describing the overall behavior of the media. Another important distinction is that connectivity metrics can either be global or localized. The global metrics are not related to a specific location while the localized metrics relate to one or several specific points in the field. Using these metrics to characterize a given aquifer requires the possibility to measure dynamic connectivity metrics in the field, to relate them with static connectivity metrics, and to constrain models with those information. Some tools are already available for these different steps and reviewed here, but they are not yet routinely integrated in practical applications. This is why new steps should be added in hydrogeological studies to infer the connectivity structure and to better constrain the models. These steps must include specific field methodologies, interpretation techniques, and modeling tools to provide more realistic and more reliable forecasts in a broad range of applications.     

A mathematical hysteretic model for elastomeric isolation bearings

An analytical model for high damping elastomeric isolation bearings is presented in this paper. The model is used to describe mathematically the damping force and restoring force of the rubber material and bearing. Ten parameters to be identified from cyclic loading tests are included in the model. The sensitivity of the ten parameters in affecting the model is examined. These ten parameters are functions of a number of influence factors on the elastomer such as the rubber compound, Mullins effect, scragging effect, frequency, temperature and axial load. In this study, however, only the Mullins effect, scragging effect, frequency and temperature are investigated. Both material tests and shaking table tests were performed to validate the proposed model. Based on the comparison between the experimental and the analytical results, it is found that the proposed analytical model is capable of predicting the shear force–displacement hysteresis very accurately for both rubber material and bearing under cyclic loading reversals. The seismic response time histories of the bearing can also be captured, using the proposed analytical model, with a practically acceptable precision. Copyright © 2002 John Wiley & Sons, Ltd.     

Calibration of a hysteretic model for glass fiber reinforced gypsum wall panels

Glass fi ber reinforced gypsum(GFRG) wall panels are prefabricated panels with hollow cores, originally developed in Australia and subsequently adopted by India and China for use in buildings. This paper discusses identifi cation and calibration of a suitable hysteretic model for GFRG wall panels fi lled with reinforced concrete. As considerable pinching was observed in the experimental results, a suitable hysteretic model with pinched hysteretic rule is used to conduct a series of quasi-static as inelastic hysteretic response analyses of GFRG panels with two different widths. The calibration of the pinching model parameters was carried out to approximately match the simulated and experimental responses up to 80% of the peak load in the post peak region. Interestingly, the same values of various parameters(energy dissipation and pinching related parameters) were obtained for all fi ve test specimens.     

Accuracy of kinematic wave and diffusion wave approximations for space-independent flows on infiltrating surfaces

Error equations for the kinematic wave and diffusion wave approximations were derived under simplified conditions for space-independent flows occurring on infiltrating planes or channels. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions were parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel bed slope, lateral inflow and channel roughness when the initial condition is non-vanishing; it reflects the effect of bed slope, channel roughness, lateral inflow and infiltration when the initial condition is vanishing. The error equations were found to be the Riccati equation.     

Cyclic hysteretic flow in porous medium column: model, experiment, and simulations

A periodic vertical movement of the groundwater table results in a subsequent cyclic response of the water content and pressure profiles in the vadose zone. The sequence of periodic wetting and drying processes can be affected by hysteresis effects in this zone. A one-dimensional saturated/unsaturated flow model based on Richards’ equation and the Mualem (Soil Sci. 137 (1984) 283) hysteresis model is formulated which can take into account multi-cycle hysteresis effects in the relation between capillary pressure and water content. The numerical integration of the unsaturated flow equation is based on a Galerkin-type finite element method. The flow domain is discretised by finite elements with linear shape functions. Simulations start with static water content and pressure profiles, which correspond to either a boundary drying or wetting retention curve. To facilitate the numerical solution of the hysteretic case an implicit non-iterative procedure was chosen for the solution of the nonlinear differential equation. Laboratory experiments were performed with a vertical sand column by imposing a high frequency periodic pressure head at the lower end of the column. The total water volume in the column, and the periodic water content profile averaged over time were measured. The boundary drying and wetting curves of the relation between water content and capillary pressure were determined by independent experiments. The simulations of the experimental conditions show a clear effect of the hysteresis phenomenon on the water content profile. The simulations with hysteresis agree well with the measurements. Computed dimensionless water content profiles are presented for different oscillation frequencies with and without consideration of hysteresis.     

Nonlinear iteration methods for nonequilibrium multiphase subsurface flow

Fully implicit, fully coupled techniques are developed for simulating multiphase flow with nonequilibrium mass transfer between phases, with application to groundwater contaminant flow and transport. Numerical issues which are addressed include: use of MUSCL or Van Leer flux limiters to reduce numerical dispersion, use of full or approximate Jacobian for flux limiter methods, and variable substitution for increased Newton iteration efficiency. A comparison of the performance of equilibrium and nonequilibrium models is also presented.     

Sparse Randomized Maximum Likelihood (SpRML) for subsurface flow model calibration and uncertainty quantification

Despite their apparent high dimensionality, spatially distributed hydraulic properties of geologic formations can often be compactly (sparsely) described in a properly designed basis. Hence, the estimation of high-dimensional subsurface flow properties from dynamic performance and monitoring data can be formulated and solved as a sparse reconstruction inverse problem. Recent advances in statistical signal processing, formalized under the compressed sensing paradigm, provide important guidelines on formulating and solving sparse inverse problems, primarily for linear models and using a deterministic framework. Given the uncertainty in describing subsurface physical properties, even after integration of the dynamic data, it is important to develop a practical sparse Bayesian inversion approach to enable uncertainty quantification. In this paper, we use sparse geologic dictionaries to compactly represent uncertain subsurface flow properties and develop a practical sparse Bayesian method for effective data integration and uncertainty quantification. The multi-Gaussian assumption that is widely used in classical probabilistic inverse theory is not appropriate for representing sparse prior models. Following the results presented by the compressed sensing paradigm, the Laplace (or double exponential) probability distribution is found to be more suitable for representing sparse parameters. However, combining Laplace priors with the frequently used Gaussian likelihood functions leads to neither a Laplace nor a Gaussian posterior distribution, which complicates the analytical characterization of the posterior. Here, we first express the form of the Maximum A-Posteriori (MAP) estimate for Laplace priors and then use the Monte-Carlo-based Randomize Maximum Likelihood (RML) method to generate approximate samples from the posterior distribution. The proposed Sparse RML (SpRML) approximate sampling approach can be used to assess the uncertainty in the calibrated model with a relatively modest computational complexity. We demonstrate the suitability and effectiveness of the SpRML formulation using a series of numerical experiments of two-phase flow systems in both Gaussian and non-Gaussian property distributions in petroleum reservoirs and successfully apply the method to an adapted version of the PUNQ-S3 benchmark reservoir model.     

Dual-porosity and kinematic wave approaches to assess the degree of preferential flow in an unsaturated soil

Abstract

The purpose of this study was to assess the degree of preferential flow in an unsaturated soil column using two different models: the dual-porosity model, MACRO, and the kinematic wave approach (KWA) based on boundary-layer flow theory. The soil column experiments consisted of six infiltrations with intensities varying from 15 to 101 mm h^?1. Bromide solution was also infiltrated at an intensity of 79 mm h^?1 and a concentration of 80 mg l^?1. Both MACRO and the KWA indicated the absence of pure preferential flow. The KWA indicated intermediate flow with dispersion of the wetting front with depth, whereas MACRO indicated flow dominated by the diffusion of capillary potential. These results shed light on the transition between flows dominated by momentum dissipation and by diffusion of capillary potential. The absence of pure macropore flow in the structured sandy soil is mainly due to efficient lateral mass exchange in this material.