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1.
《水文科学杂志》2013,58(2):349-362
Abstract A methodology of time-step estimation for numerically solving the Richards equation is discussed. Its importance in simulating water movement in unsaturated—saturated soils is shown for infiltration into a soil profile by applying various time-step estimations and boundary conditions for different soils. In order to test the results of the computations, infiltration theory was applied. According to infiltration theory, the pressure head in the initially unsaturated part will not take positive values as long as the moisture front has not reached the phreatic level, or, in the case of a profile with a free-draining lower boundary, it is not saturated at the base. In other cases, the appearance of positive values of the pressure head produces incorrect values for the inflow rate q. 相似文献
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Abstract Numerical simulations of internal gravity waves-turbulence are carried out for the inviscid, viscous and forced-dissipative two-dimensional primitive equations using the spectral method. Some of the results are compared with the predictions of the eddy damped quasi-normal Markovian (EDQNM) closure for internal waves of Carnevale and Frederiksen, generalized for periodic boundary conditions and possible random forcing and dissipation. The EDQNM reduces to the Boltzman equation of resonant interaction theory in the continuum space limit and as the forcing and dissipation vanish. However, the limit is singular in the sense that as well as conserving total energy, E, and total cross-correlation between the vorticity and buoyancy fields, C, an additional conservation law, viz. z-momentum, Pz , occurs in the limit. This means that the resonant interaction equilibrium (RIE) solution of the Boltzmann equation differs from the statistical mechanical equilibrium (SME) solution of the EDQNM closure. The statistical stability of the SME and RIE spectra for the primitive equations is tested by integrating the inviscid equations using initial realizations of these spectra with random phases. It is found that E and C are accurately conserved while Pz undergoes large amplitude variations. The approach to equilibrium of initial disequilibrium spectra is monitored by examining the evolution of the entropy. The increase and asymptotic approach to a constant value corresponding to complete chaos is consistent with the behaviour predicted by the EDQNM closure. For the viscous decay and forced-dissipative experiments, the behaviour of the entropy is also consistent with that predicted by the EDQNM closure. There is approximate equipartition of potential and total kinetic energies throughout the integrations from initial conditions having equal potential and total kinetic energies and as well equal vertical and horizontal energies, but as expected, the ratio of horizontal to vertical kinetic energy increases with time to a value greater than unity. With Laplacian viscous dissipation and thermal diffusivity, the statistical steady states produced in the forced-dissipative experiments have k?3 power laws for k≧7. A comparison with the power laws for kinetic energy and passive scalar variance produced in a numerical simulation of the two-dimensional passive scalar problem is also presented. 相似文献
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Error equations for kinematic wave and diffusion wave approximations were derived for time‐independent flows on infiltrating planes and channels under one upstream boundary and two downstream boundary conditions: zero flow at the upstream boundary, and critical flow depth and zero depth gradient at the downstream boundary. These equations specify error in the flow hydrograph as a function of space. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors below 2% for values of KF (e.g. KF ≥ 7·5), where K is the kinematic wave number and F is the Froude number. Even for small values of KF (e.g. KF = 2·5), the errors were typically less than 3%. The accuracy of the diffusive approximation was greatly influenced by the downstream boundary condition. For critical flow depth downstream boundary condition, the error of the kinematic wave approximation was found to be less than 10% for KF ≥ 7·5 and greater than 20% for smaller values of KF. This error increased with strong downstream boundary control. The analytical solution of the diffusion wave approximation is adequate only for small values of K. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
5.
We study path effects on prediction equations of pseudo‐velocity response spectra (natural period of 0.1–5.0 s) in northern Japan, where heterogeneous attenuation structure exists. The path effects have been examined by comparing the regression analysis results for two different prediction equations. The first equation consists of a single term of anelastic attenuation conventionally. The second equation consists of two terms of anelastic attenuation in consideration of the heterogeneous attenuation structure. In the second equation, we divide a source‐to‐site distance into two distances at the attenuation boundary beneath the volcanic front. The boundary is considered to separate the relatively high Q fore‐arc side mantle wedge (FAMW) from the low Q back‐arc side mantle wedge (BAMW). Strong motion records (hypocentral distances less than 300 km) from interplate and intraslab events with Mw 5.1–7.3 are used. Regression analysis results show that the standard errors are significantly reduced by the second prediction equation at short periods (0.1–0.5 s), whereas the difference in standard errors from both prediction equations is negligible at intermediate and long periods. The Qs values (quality factor for S‐wave) converted from two anelastic attenuation coefficients for the second prediction equation are remarkably similar to the path‐averaged Qs values for the FAMW and BAMW by other studies using spectral inversion method. From these findings, we conclude that the path effects on the prediction equation of pseudo‐velocity response spectra are satisfactorily accomplished by the second prediction equation. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
6.
The Green and Ampt infiltration formula, as well as the Talsma and Parlange formula, are two-parameter equations that are both expressible in terms of Lambert W-functions. These representations are used to derive explicit, simple and accurate approximations for each case. The two infiltration formulas are limiting cases that can be deduced from an existing three-parameter infiltration equation, the third parameter allowing for interpolation between the limiting cases. Besides the limiting cases, there is another case for which the three-parameter infiltration equation yields an exact solution. The three-parameter equation can be solved by fixed-point iteration, a scheme which can be exploited to obtain a sequence of increasingly complex explicit infiltration equations. For routine use, a simple, explicit approximation to the three-parameter infiltration equation is derived. This approximation eliminates the need to iterate for most practical circumstances. 相似文献
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A modified multiple tension upward infiltration method to estimate the soil hydraulic properties 
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下载免费PDF全文 Determination of saturated hydraulic conductivity, Ks, and the shape parameters α and n of the water retention curve, θ(h), is of paramount importance to characterize the water flow in the vadose zone. This work presents a modified upward infiltration method to estimate Ks, α and n from numerical inverse analysis of the measured cumulative upward infiltration (CUI) at multiple constant tension lower boundary conditions. Using the HYDRUS‐2D software, a theoretical analysis on a synthetic loam soil under different soil tensions (0, 0–10, 0–50 and 0–100 cm), with and without an overpressure step of 10 cm high from the top boundary condition at the end of the upward infiltration process, was performed to check the uniqueness and the accuracy of the solutions. Using a tension sorptivimeter device, the method was validated in a laboratory experiment on five different soils: a coarse and a fine sand, and a 1‐mm sieved loam, clay loam and silt‐gypseous soils. The estimated α and n parameters were compared to the corresponding values measured with the TDR‐pressure cell method. The theoretical analysis demonstrates that Ks and θ(h) can be simultaneously estimated from measured upward cumulative infiltration when high (>50 cm) soil tensions are initially applied at the lower boundary. Alternatively, satisfactory results can be also obtained when medium tensions (<50 cm) and the Ks calculated from the overpressure step at the end of the experiment are considered. A consistent relationship was found between the α (R2 = 0.86, p < 0.02) and n (R2 = 0.97, p < 0.001) values measured with the TDR‐pressure cell and the corresponding values estimated with the tension sorptivimeter. The error between the α (in logarithm scale) and n values estimated with the inverse analysis and the corresponding values measured with pressure chamber were 3.1 and 6.1%, respectively. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
Abstract This paper develops a new analytical solution for the aquifer system, which comprises an unconfined aquifer on the top, a semi-confined aquifer at the bottom and an aquitard between them. This new solution is derived from the Boussinesq equation for the unconfined aquifer and one-dimensional leaky confined flow equation for the lower aquifer using the perturbation method, considering the water table over-height at the remote boundary. The head fluctuation predicted from this solution is generally greater than the one solved from the linearized Boussinesq equation when the ratio of the tidal amplitude to the thickness of unconfined aquifer is large. It is found that both submarine groundwater discharges from upper and lower aquifers increase with tidal amplitude–aquifer thickness ratio and may be underestimated if the discharge is calculated based on the average head fluctuation. The effects of the aquifer parameters and linearization of the Boussinesq equation on the normalized head fluctuation are also investigated. Editor D. Koutsoyiannis; Associate editor J. Simunek Citation Chuang, M.-H., Mahdi, A.-A. and Yeh, H.-D., 2012. A perturbation solution for head fluctuations in a coastal leaky aquifer system considering water table over-height. Hydrological Sciences Journal, 57 (1), 162–172. 相似文献
9.
Soil water repellency induced by wildfires can alter hydraulic properties and hydrologic processes; however, the persistence and vertical position (i.e., depth) of water-repellent layers can vary between systems and fires, with limited understanding of how those variations affect infiltration processes. This study occurred in two forested locations in the south-central Appalachian Mountains that experienced wildfires in late 2016: Mount Pleasant Wildfire Refuge, Virginia, and Chimney Rock State Park, North Carolina. In each location, sites were selected to represent unburned conditions and low to moderate burn intensities. At each site, we measured the soil water repellency at the surface (ash layer or O horizon) and ~2 cm below the surface (A horizon) using the water drop penetration time method (n = 10–14). Soil water content was also measured over the upper 10 cm of the soil (n = 10), and infiltration tests were conducted using a tension infiltrometer (n = 6–8). The results showed that soil repellency was highest in the surface layer at the Mount Pleasant location and was highest in the subsurface layer at the Chimney Rock location. Soil water content was lower in unburned soil than in burned soil, especially for measurements taken immediately postfire, with soil water content negatively correlated with water repellency. Water repellency in the surface layer significantly reduced relative infiltration rates (estimated as differences between initial and steady-state rates), whereas subsurface water repellency did not affect relative infiltration. As a result, water repellency persisted longer in sites with surface as opposed to subsurface water repellency. Finally, differences between burned and unburned sites showed that although the wildfires increased the occurrence of water repellency, they did not alter the underlying relationship between relative infiltration and water repellency of the surface soil. 相似文献
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Summary A new computation method is described which determines the focal coordinates, theP
n-andP
G-velocity, the focal time and the Moho-depth in the case of near earthquakes. The method is provided especially for areas where the crustal parameters are insufficiently known. It presumes that the standard error ofP
n-andP
G-arrival times is a minimum. The problem turns out to represent the solution of a set of at least seven equations with seven unknown parameters. Four of these unknowns can be separated in advance. This leads to a considerable simplification. The three remaining unknowns are the focal coordinates. Their best fitting values are found by the gradient method. An example is presented which shows how errors can arise if the initial trial coordinate is chosen at an unfavourable position. 相似文献
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Vincenzo Alagna Massimo Iovino Vincenzo Bagarello Jorge Mataix‐Solera Lubomir Lichner 《水文研究》2019,33(4):661-674
The repellency index (RI) defined as the adjusted ratio between soil‐ethanol, Se, and soil‐water, Sw, sorptivities estimated from minidisk infiltrometer experiments has been used instead of the widely used water drop penetration time and molarity of ethanol drop tests to assess soil water repellency. However, sorptivity calculated by the usual early‐time infiltration equation may be overestimated as the effects of gravity and lateral capillary are neglected. With the aim to establish the best applicative procedure to assess RI, different approaches to estimate Se and Sw were compared that make use of both the early‐time infiltration equation (namely, the 1 min, S1, and the short‐time linearization approaches), and the two‐term axisymmetric infiltration equation, valid for early to intermediate times (namely, the cumulative linearization and differentiated linearization approaches). The dataset included 85 minidisk infiltrometer tests conducted in three sites in Italy and Spain under different vegetation habitats (forest of Pinus pinaster and Pinus halepensis, burned pine forest, and annual grasses), soil horizons (organic and mineral), postfire treatments, and initial soil water contents. The S1 approach was inapplicable in 42% of experiments as water infiltration did not start in the first minute. The short‐time linearization approach yielded a systematic overestimation of Se and Sw that resulted in an overestimation of RI by a factor of 1.57 and 1.23 as compared with the cumulative linearization and differentiated linearization approaches. A new repellency index, RIs, was proposed as the ratio between the slopes of the linearized data for the wettable and hydrophobic stages obtained by a single water infiltration test. For the experimental conditions considered, RIs was significantly correlated with RI and WDPT. Compared with RI, RIs includes information on both soil sorptivity and hydraulic conductivity and, therefore, it can be considered more physically linked to the hydrological processes affected by soil water repellency. 相似文献
13.
C. VENETIS 《水文科学杂志》2013,58(4):119-125
Abstract The dependence of the recession of the ground water levels and the ground water discharge upon the initial state of the aquifer is examined for deep unconfined aquifers. It is shown that only in the early stages of the recession does the initial state exert a limited influence on the recession. An estimate of the upper limit of the time t 0 for which for t > t 0 the recession becomes effectively independent of the initial state of the aquifer, valid for physically realistic initial states can be gained from inequalities (11) and (12a) and equation (16). t 0 depends essentially on the parameters of the aquifer and it is estimated that for useful aquifers t 0 can not be expected to exceed one month in relatively adverse cases. This explains why empirical recessions often are found to be consistent, of an exponential form. 相似文献
14.
Andy Louwyck Alexander Vandenbohede Griet Heuvelmans Marc Van Camp Kristine Walraevens 《Ground water》2023,61(1):100-110
The water budget myth, which is the idea that safe pumping must not exceed the initial recharge, gave rise to a controversy about the role of recharge in assessing the sustainability of groundwater development. To refute the concept of safe yield, a simplified water budget equation is used, which equals the total pumping rate to the sum of capture and storage change. Since initial recharge and discharge are canceled out from this equation, it is concluded that sustainable pumping has nothing to do with recharge. Investigating the assumptions underlying this equation, it is seen that it expresses the superposition principle, which implicitly assumes the groundwater reservoir can be depleted indefinitely and boundary conditions are an infinite source of water. To evaluate sustainability, however, the limits of the aquifer system must be examined accurately. Theoretically, this can only be accomplished applying nonlinear models, in which case setting up the simplified water budget equation is impossible without knowing the initial conditions. Hence, excluding recharge when assessing sustainable pumping may not be done inconsiderately, which is illustrated by two examples. An analytical solution, developed by Ernst in 1971 to simulate flow to a well in a polder area with a nonlinear function for drainage, even shows that it is not necessarily a misconception to assume the cone of depression stops expanding when the pumping rate is balanced by the infiltration rate. 相似文献
15.
The cross-sectional stability of double inlet systems is investigated using an exploratory model that combines Escoffier’s stability concept for the evolution of the inlet’s cross-sectional area with a two-dimensional, depth-averaged (2DH) hydrodynamic model for tidal flow. The model geometry consists of four rectangular compartments, each with a uniform depth, associated with the ocean, tidal inlets and basin. The water motion, forced by an incoming Kelvin wave at the ocean’s open boundary and satisfying the linear shallow water equations on the f -plane with linearised bottom friction, is in each compartment written as a superposition of eigenmodes, i.e. Kelvin and Poincaré waves. A collocation method is employed to satisfy boundary and matching conditions. The analysis of resulting equilibrium configurations is done using flow diagrams.
Model results show that internally generated spatial variations in the water motion are essential for the existence of stable equilibria with two inlets open. In the hydrodynamic model used in the paper, both radiation damping into the ocean and basin depth effects result in these necessary spatial variations. Coriolis effects trigger an asymmetry in the stable equilibrium cross-sectional areas of the inlets. Furthermore, square basin geometries generally correspond to significantly larger equilibrium values of the inlet cross-sections. These model outcomes result from a competition between a destabilising (caused by inlet bottom friction) and a stabilising mechanism (caused by spatially varying local pressure gradients over the inlets).
相似文献16.
《水文科学杂志》2013,58(4):700-712
Abstract The groundwater flow equation governing the elevation (h) of the steady-state phreatic surface in a sloping aquifer fed by constant recharge over a bi-circular sector is rhh′ ? r 2 Bh′ + Pr 2 ? PR 2 = 0, where r is the radial coordinate, P is a constant involving recharge and aquifer properties, and B is the slope of the aquifer—bedrock boundary. The derived flow equation describes radially convergent flow through a sloping aquifer that discharges to a water body of fixed head. One important simplification is that in which the width of the bi-circular sector is constant, and the draining land becomes a rectangular aquifer. The bi-circular sector and rectangular-strip groundwater flow problems are solved in terms of implicit equations. The solutions for the steady-state phreatic surfaces depend on the ratio of recharge to hydraulic conductivity, the slope of the aquifer-bedrock, and the downstream constant-head boundary. Computational examples illustrate the application of the solutions. 相似文献
17.
The errors in surface runoff prediction by neglecting the relationship between infiltration rate and overland flow depth 总被引：9，自引：0，他引：9
Many simplifications are used in modeling surface runoff over a uniform slope. A very common simplification is to determine the infiltration rate independent of the overland flow depth and to combine it afterward with the kinematic-wave equation to determine the overland flow depth. Another simplication is to replace the spatially variable infiltration rates along the slope i(x, t) due to the water depth variations h(x,t) with an infiltration rate that is determined at a certain location along the slope. The aim of this study is to evaluate the errors induced by these simplications on predicted infiltration rates, overland flow depths, and total runoff volume. The error analysis is accomplished by comparing a simplified model with a model where the interaction between the overland flow depth and infiltration rate is counted. In this model, the infiltration rate is assumed to vary along the slope with the overland flow depth, even for homogeneous soil profiles. The kinematic-wave equation with interactive infiltration rate, calculated along the slopy by Richard's equation, are then solved by a finite difference scheme for a 100-m-long uniform slope. In the first error analysis, we study the effect of combining an ‘exact’ and ‘approximate’ one-dimensional infiltration rate with the kinematic-wave equation for three different soil surface roughness coefficients. The terms ‘exact’ and ‘approximate’ stand for the solution of Richard's equation with and without using the overland flow depth in the boundary condition, respectively. The simulations showed that higher infiltration rates and lower overland flow depths are obtained during the rising stage of the hydrograph when overland flow depth is used in the upper boundary condition of the one-dimensional Richard's equation. During the recession period, the simplified model predicts lower infiltration rates and higher overland flow depths. The absolute relative errors between the ‘exact’ and ‘approximate’ solutions are positively correlated to the overland flow depths which increase with the soil surface roughness coefficient. For this error analysis, the relative errors in surface runoff volume per unit slope width throughout the storm are much smaller than the relative errors in momentary overland flow depths and discharges due to the alternate signs of the deviations along the rising and falling stages. In the second error analysis, when the spatially variable infiltration rate along the slope i(x, t) is replaced in the kinematic-wave equation by i(t), calculated at the slope outlet, the overland flow depth is underestimated during the rising stage of the hydrograph and overestimated during the falling stage. The deviations during the rising stage are much smaller than the deviations during the falling stage, but they are of a longer duration. This occurs because the solution with i(x, t) recognizes that part of the slope becomes dry after rainfall stops, while overland flow still exists with i(t) determined at the slope outlet. As obtained for the first error analysis, the relative errors in surface runoff volume per unit slope width are also much smaller than the relative errors in momentary overland flow depths and discharges. The relation between the errors in overland flow depth and discharge to different mathematical simplifications enables to evaluate whether certain simplifications are justified or more computational efforts should be used. 相似文献
18.
Christina Schornberg Christian Schmidt Edda Kalbus Jan H. Fleckenstein 《Advances in water resources》2010
Analytical solutions to the one-dimensional heat transport equation for steady-state conditions can provide simple means to quantify groundwater surface water exchange. The errors in exchange flux calculations that are introduced when the underlying assumptions of homogeneous sediments and constant temperature boundary conditions are violated were systematically evaluated in a simulation study. Temperatures in heterogeneous sediments were simulated using a numerical model. Heterogeneity in the sediments was represented by discrete, binary geologic units. High contrasts between the hydraulic conductivities (K) of the geologic units were found to lead to large errors, while the influence of the structural arrangement of the units was smaller. The effects of transient temperature boundary conditions were investigated using an analytical equation. Errors introduced by transient boundary conditions were small for Darcy-velocities > 0.1 m d− 1 in the period near maximum and minimum annual surface water temperatures. For smaller fluxes, however, errors can be large. Assuming steady-state conditions and vertical flow in homogeneous sediments is acceptable at certain times of the year and for medium to high exchange fluxes, but pronounced geologic heterogeneity can lead to large errors. 相似文献
19.
《水文科学杂志》2013,58(4):868-882
Abstract Non-Darcian flow in a finite fractured confined aquifer is studied. A stream bounds the aquifer at one side and an impervious stratum at the other. The aquifer consists of fractures capable of transmitting water rapidly, and porous blocks which mainly store water. Unsteady flow in the aquifer due to a sudden rise in the stream level is analysed by the double-porosity conceptual model. Governing equations for the flow in fractures and blocks are developed using the continuity equation. The fluid velocity in fractures is often too high for the linear Darcian flow so that the governing equation for fracture flow is modified by Forcheimer's equation, which incorporates a nonlinear term. Governing equations are coupled by an interaction term that controls the quasi-steady-state fracture—block interflow. Governing equations are solved numerically by the Crank-Nicolson implicit scheme. The numerical results are compared to the analytical results for the same problem which assumes Darcian flow in both fractures and blocks. Numerical and analytical solutions give the same results when the Reynolds number is less than 0.1. The effect of nonlinearity on the flow appears when the Reynolds number is greater than 0.1. The higher the rate of flow from the stream to the aquifer, the higher the degree of nonlinearity. The effect of aquifer parameters on the flow is also investigated. The proposed model and its numerical solution provide a useful application of nonlinear flow models to fractured aquifers. It is possible to extend the model to different types of aquifer, as well as boundary conditions at the stream side. Time-dependent flow rates in the analysis of recession hydrographs could also be evaluated by this model. 相似文献
20.
《水文科学杂志》2013,58(3):481-486
Abstract Explicit algebraic expressions of influence coefficients of an aquifer system are addressed. The methodology is straightforwardly exemplified using a one-dimensional (1D) semi-confined homogeneous aquifer model. It consists of the integration of the governing equation from two different viewpoints. On the one hand, the analytical solution to the governing equation is presented under an integral form involving the appropriate Green function. On the other hand, equations resulting from a finite difference discretization are processed to deduce a fully explicit algebraic expression of the nodal hydraulic head. This latter, arranged after the previously developed continuum solution, helps with deriving an explicit algebraic expression of influence coefficients corresponding to the studied aquifer model. Finally, the study is extended to an inhomogeneous aquifer model. 相似文献