摘要:

We consider advective transport in a steady state random velocity field with homogeneous increments. Such a field is self‐affine with a power law dyadic semivariogram γ(s) proportional tod2ω, wheredis distance and ω is a Hurst coefficient. It is characterized by a fractal dimensionD=E+ 1 − ω, whereEis topological dimension. As the mean and variance of such a field are undefined, we condition them on measurement at some pointx0. We then introduce a tracer at another pointy0and invoke elementary theoretical considerations to demonstrate that its conditional mean dispersion is local at all times. Its conditional mean concentration and variance are given explicitly by well‐established expressions which, however, have not been previously recognized as being valid in fractal fields. Once the conditional mean travel distancesof the tracer becomes large compared to the distance betweeny0andx0, the corresponding dispersion and dispersivity tensors grow in proportion tos1+2ω, where 0<ω<1. This supralinear rate of growth is consistent with that exhibited by apparent longitudinal dispersivities obtained by standard methods of interpretation from tracer behavior observed in a variety of geologic media under varied flow and transport regimes. Filtering out modes from the fractal velocity field with correlation scales larger than somes0allows an asymptotic transport regime to develop whens≫s0. The corresponding asymptotic dispersivities grow in proportion tos02ω, when 0<ω ≤ ½. This linear to sublinear rate of growth is consistent with that exhibited by apparent longitudinal dispersivities obtained from calibrated numerical models in a variety of media. A self‐affine natural log permeability field gives rise to a self‐affine velocity field, whilesis sufficiently small to insure that the variance of the log permeabilities, which grows as a power ofs, remains nominally less than one. An analysis of published apparent longitudinal dispersivity data in light of the above theoretical results supports my earlier conclusion that when one juxtaposes data from a large number of generally dissimilar geologic media from a variety of locales, one observes a tendency toward self‐affine behavior with a Hurst coefficient ω ≃ 0.25. At any given locale such media may or may not exhibit fractal behavior; if they do, ω may

ISSN:0043-1397    

DOI:10.1029/95WR00426

年代:1995

数据来源: WILEY

摘要:

A key characterization of dispersion in aquifers and other porous media has been to map the effects of inhomogeneous velocity fields onto a Fickian dispersion term (D) within the context of the conventional advection‐dispersion equation (ADE). Recent compilations of data have revealed, however, that the effectiveDcoefficient is not constant but varies systematically with the length or timescale over which transport occurs. A natural strategy to encompass this “anomalous” behavior into the context of the conventional ADE is to makeDtime dependent. This approach, to useD(t) to handle the same anomalous dispersion phenomena, has also been common in the field of electronic transport in disordered materials. In this paper we discuss the intrinsic inadequacy of considering a time‐dependent dispersivity in the conventional ADE context, and show that theD=D(t) generalization leads to quantifiably incorrect solutions. In the course of proving this result we discuss the nature of anomalous dispersion and provide physical insight into this important problem in hydrogeology via analysis of a class of kinetic approaches. Particular emphasis is placed on the effects of a distribution of solute “delay times” with a diverging mean time, which we relate to configurations of preferential pathways in heteroge

ISSN:0043-1397    

DOI:10.1029/95WR00483

年代:1995

数据来源: WILEY

摘要:

Model validation is still a crucial issue in hydrology. It is usually limited to comparing simulated and measured streamflows, while many other fluxes and storages are also simulated. This is especially true for spatially distributed models, for which multivariable and multiscale validation procedures are needed. Such an approach has been tested on the Fecht research basin (Vosges Massif, France) over a 5‐year period, using the semidistributed conceptual MC model, whose physical soundness has been improved. The catchment discretization into land units was based on simple physiographic criteria, which were statistically validated. Water balance parameters were derived from measured soil water retention, without any calibration. Catchment streamflow was used to calibrate water transfer parameters over a single year and validate the model. Two subcatchments were used for the internal validation, and two neighboring nested catchments were used for the regional transposition of both the model and its distributed parameterization. At the mesh scale (250 to 1000 m), snowpack and soil water storages and contribution to streamflow were validated by using measurements from two small catchments. Despite the very limited calibration, the results were generally satisfactory. Nash‐Sutclifife efficiencies on daily streamflow varied from 0.92 in calibration to 0.89 in validation and 0.71 in transposition. The results of the simulated patterns of fluxes and storages can therefore be considered with some confide

ISSN:0043-1397    

DOI:10.1029/94WR03293

年代:1995

数据来源: WILEY

摘要:

Tritiated water, released at a point in a uniform, relatively dry soil, diffuses in both the liquid and vapor phases. A model which accords well with published data indicates that the flux density of tritium in the liquid exceeds that in the vapor phase provided the water content is greater than approximately 20% of the total soil porosity. Thus tritium redistribution should be modeled recognizing transfer “in parallel” in both phases. The diffusion equation cast in spherical coordinates, and taking into account radioactive decay, then provides a basis for design of field experiments and predicts the long‐term fate of tritiated water released in these experiments. We calculate the evolution of profiles of tritium concentration, within and external to the sphere of released solution, assuming the initial concentration to be uniform. We also predict the speed and the envelope of the tritium maximum as it advances and attenuates in the soil. We briefly discuss effects of variation in the volume fractions of soil water and air on the effective diffusion coefficient of tritium in soil and comment on possible effects of convective transfer by moving water an

ISSN:0043-1397    

DOI:10.1029/94WR02013

年代:1995

数据来源: WILEY

摘要:

High‐permeability faults, acting as preferential pathways for fluid migration, are important geological structures for fluid, energy, and solute transport. This paper examines the interaction of thermally driven convective circulation in a steeply dipping fault zone and groundwater flow through the surrounding country rock that is driven by a regional topographic gradient. We consider a geometry where a fault zone with a homogeneous, isotropic permeability is located beneath a narrow valley in a region with substantial topographic relief. System behavior is best characterized in terms of the large‐scale permeabilities of the country rock and the fault zone. Using three‐dimensional numerical simulations, we map in permeability space four fluid flow and heat transfer regimes within a fault zone: conductive, advective, steady convective, and unsteady convective. The patterns of fluid flow and/or heat transfer are substantially different in each of these regimes. Maximum discharge temperatures can also be plotted in permeability space; the maximum discharge temperature in the advective regime is in general lower than that in the steady convective regime. A higher basal heat flux expands the convective regime in permeability space, as does a greater fault depth. Higher topographic relief on the regional water table compresses the convective regime, with the advective regime suppressing convective circulation at lower country rock permeabilities. If convective cells with aspect ratios close to 1 cannot form, the steady convective regime is smaller in permeability space, and the boundary between steady and unsteady convection occurs at lower values of fault zone permeability. At low country rock permeabilities a water table gradient along the surface trace of the fault of approximately 0.3% suppresses convective cells; at higher country rock permeabilities, convection can be suppressed by smaller gradients on the water

ISSN:0043-1397    

DOI:10.1029/95WR00422

年代:1995

数据来源: WILEY

摘要:

A new first‐order analytical solution for stochastic transport of reactive solutes in physically and chemically heterogeneous porous formations is derived and discussed. Physical and chemical heterogeneities are assumed partially correlated. The derived solution complements previous results obtained by the authors (Bellin et al., 1993). The solution proposed relies on the assumption of chemical activity described by the local linear equilibrium assumption postulating the existence of a (spatially variable) retardation factor. Retardation factors,R(x) and log permeabilities (Y(x)) modeling heterogeneities are described statistically by random space functions with assigned correlation structure. The analytical expressions derived reduce to Dagan's (1984) classic solution for the case of nonreactive solute transport and to Bellin et al.'s (1993) solutions for perfectly correlated physical and chemical heterogeneities. The main conclusion is that longitudinal dispersion may be significantly affected by different degrees of correlation between chemical and physical heterogeneities. However, such an impact vanishes progressively as the geometric mean of the partition coefficient increases and the plume behaves as in perfectly correlated cases. Transverse dispersion is not affected by either perfect or partial correlation betweenRand

ISSN:0043-1397    

DOI:10.1029/95WR00200

年代:1995

数据来源: WILEY

摘要:

Several attempts have been made in the past to model hydrological processes such as monthly streamflows in dry regions. One of the crucial problems in modeling this type of process is the handling of zero flows. A stochastic model is presented herein which enables the reproduction of the percentage of zero flows in each month, the monthly mean and variance, and the month‐to‐month correlation of the intermittent flows. The model considers the intermittent monthly flow process as a product of a periodic binary discrete process and a periodic continuous process. Both the discrete and the continuous processes are periodic first‐order autoregressive. Parameter estimation has been developed based on the method of moments, method of transition probability, and method of maximum likel

ISSN:0043-1397    

DOI:10.1029/95WR00144

年代:1995

数据来源: WILEY

摘要:

Rainfall‐runoff models of the black box type abound in the water resources literature (i.e., transfer function, autoregressive moving average (ARMA), ARMAX, state space, etc.). The corresponding system identification algorithms for such models are known to be numerically efficient and accurate, leading in most cases to good parsimonious representations of the rainfall‐runoff process. Alternatively, every model in transfer function, ARMA, and ARMAX form has an equivalent state space representation. However, state space models do not necessarily have simple system identification algorithms, unless the system matrices are restricted to some canonical form. Furthermore, state space system identification algorithms that work with the rainfall/runoff data directly (i.e., covariance free), require initial conditions and are inherently iterative and nonlinear. In this paper we present a state space system identification theory which overcomes these limitations. One advantage of such a theory is that the corresponding algorithms are highly robust to additive noise in the data. They are referred to as “subspace algorithms” due to their ability to separate the signal subspace from the noise subspace. The main advantages of the subspace algorithms are the automatic structure identification (system order), geometrical insights (notions of angle between subspaces), and the fact that they rely on robust numerical procedures (singular value decomposition). In this paper, two algorithms are presented. The first one is a two‐step procedure, where the impulse response (unit hydrograph ordinates for the single‐input, single‐output case) are computed from the input/output data by solving a constrained deconvolution problem. These impulse response ordinates are then used as inputs for identifying the system matrices by means of a Hankel‐based realization algorithm. The second approach uses the data directly to identify the system matrices, bypassing the deconvolution step. The algorithms are tested with real data from the Voer catch

ISSN:0043-1397    

DOI:10.1029/95WR00234

年代:1995

数据来源: WILEY

摘要:

The variability in Hortonian surface runoff discharge and volume produced by stationary rainstorms on watersheds with spatially distributed soil saturated hydraulic conductivity is examined using a two‐dimensional runoff model and a Monte Carlo methodology. Results indicate that rainfall durationtr, rainfall intensityi, representative time to equilibriumtre, mean saturated hydraulic conductivityKm, and coefficient of variationCυplay major roles in the variability of surface runoff. Similarity in surface runoff generated on heterogeneous soils is governed by the following dimensionless parameters:T* =tr/tre,K* =Km/i, andCυ. The variability in both discharge and runoff volume for randomly distributed systems increases withK* andCυ, compared to the runoff generated from uniformly distributed systems. Runoff variability decreases whenT* increases unless the mean value of hydraulic conductivity approaches the rainfall intensity (K* → 1). In highly pervious watersheds the steady state discharge depends on the spatial distribution of hydraulic conductivity. Lumped values of saturated hydraulic conductivity are found to typically underestimate the peak discharge and runoff

ISSN:0043-1397    

DOI:10.1029/95WR00518

年代:1995

数据来源: WILEY

摘要:

The influence of storm motion on runoff is explored, with a focus on dimensionless hydrologic similarity parameters. One‐ and two‐dimensional physically based runoff models are subjected to moving rainstorms. A dimensionless storm speed parameterUte/Lp, whereUis the storm speed,teis the runoff plane kinematic time to equilibrium, andLpis the length of the runoff plane, is identified as a similarity condition. Storm motion effects on the peak discharge are greatest when the storm is traversing a one‐dimensional runoff plane in the downslope direction at a dimensionless speed ofUte/Lp= 0.5. This conclusion holds for all values of the dimensionless storm sizesLs/LpwhereLsis the length of the storm in the direction of motion. Simulations with a two‐dimensional rainfall‐runoff model confirm the applicability of this similarity parameter on natural watershed topography. Results indicate that the detailed simulation of storm motion is necessary when the storm is moving near the velocity of maximum effect, which is considerably slower than typical storm v

ISSN:0043-1397    

DOI:10.1029/95WR00519

年代:1995

数据来源: WILEY