Showing papers in "Water Resources Research in 1993"

How much complexity is warranted in a rainfall-runoff model?

Abstract: Development of mathematical models relating the precipitation incident upon a catchment to the streamflow emanating from the catchment has been a major focus of surface water hydrology for decades. Generally, values for parameters in such models must be selected so that runoff calculated from the model “matches” recorded runoff from some historical period. Despite the fact that the physics governing the path of a drop of water through a catchment to the stream involves complex relationships, evidence indicates that the information content in a rainfall-runoff record is sufficient to support models of only very limited complexity. This begs the question of what limits the observed data place on the allowable complexity of rainfall-runoff models. Time series techniques are applied for estimating transfer functions to determine how many parameters are appropriate to describe the relationship between precipitation and streamflow in the case where data on only precipitation, air temperature, and streamflow are available. Statistics from an “information matrix” provide the clues necessary for determining allowable model complexity. Time series models are developed for seven catchments with widely varying physical characteristics in different temperate climatic regimes to demonstrate the method. It is found that after modulating the measured rainfall using a nonlinear loss function, the rainfall-runoff response of all catchments is well represented using a linear model. Also, for all catchments a two-component linear model with four parameters is the model of choice. The two components can be interpreted as defining a “quick flow” and “slow flow” response of the given catchment. The method therefore provides a statistically rigorous way to separate hydrographs and parameterize their response behavior. The ability to construct reliable transfer function models for describing the rainfall-runoff process offers a new approach to investigate empirically the controls of physical catchment descriptors, land use change, climate change, etc., on the dynamic response of catchments through the extensive analysis of historical data sets.

A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media

Abstract: A one-dimensional dual-porosity model has been developed for the purpose of studying variably saturated water flow and solute transport in structured soils or fractured rocks. The model involves two overlaying continua at the macroscopic level: a macropore or fracture pore system and a less permeable matrix pore system. Water in both pore systems is assumed to be mobile. Variably saturated water flow in the matrix as well as in the fracture pore system is described with the Richards' equation, and solute transport is described with the convection-dispersion equation. Transfer of water and solutes between the two pore regions is simulated by means of first-order rate equations. The mass transfer term for solute transport includes both convective and diffusive components. The formulation leads to two coupled systems of nonlinear partial differential equations which were solved numerically using the Galerkin finite element method. Simulation results demonstrate the complicated nature of solute leaching in structured, unsaturated porous media during transient water flow. Sensitivity studies show the importance of having accurate estimates of the hydraulic conductivity near the surface of soil aggregates or rock matrix blocks. The proposed model is capable of simulating preferential flow situations using parameters which can be related to physical and chemical properties of the medium.

Some statistics useful in regional frequency analysis

Abstract: Regional frequency analysis uses data from a number of measuring sites. A “region” is a group of sites each of which is assumed to have data drawn from the same frequency distribution. The analysis involves the assignment of sites to regions, testing whether the proposed regions are indeed homogeneous, and choice of suitable distributions to fit to each region's data. This paper describes three statistics useful in regional frequency analysis: a discordancy measure, for identifying unusual sites in a region; a heterogeneity measure, for assessing whether a proposed region is homogeneous; and a goodness-of-fit measure, for assessing whether a candidate distribution provides an adequate fit to the data. Tests based on the statistics provide objective backing for the decisions involved in regional frequency analysis. The statistics are based on the L moments [Hosking, 1990] of the at-site data.

Channel network source representation using digital elevation models

Abstract: Methods for identifying the size, or scale, of hillslopes and the extent of channel networks from digital elevation models (DEMs) are examined critically. We show that a constant critical support area, the method most commonly used at present for channel network extraction from DEMs, is more appropriate for depicting the hillslope/valley transition than for identifying channel heads. Analysis of high-resolution DEMs confirms that a constant contributing area per unit contour length defines the extent of divergent topography, or the hillslope scale, although there is considerable variance about the average value. In even moderately steep topography, however, a DEM resolution finer than the typical 30 m by 30 m grid size is required to accurately resolve the hillslope/valley transition. For many soil-mantled landscapes, a slope-dependent critical support area is both theoretically and empirically more appropriate for defining the extent of channel networks. Implementing this method for overland flow erosion requires knowledge of an appropriate proportionality constant for the drainage area-slope threshold controlling channel initiation. Several methods for estimating this constant from DEM data are examined, but acquisition of even limited field data is recommended. Finally, the hypothesis is proposed that an inflection in the drainage area-slope relation for mountain drainage basins reflects a transition from steep debris flow-dominated channels to lower-gradient alluvial channels.

Thermodynamic basis of capillary pressure in porous media

Abstract: Important features of multiphase flow in porous media that distinguish it from single-phase flow are the presence of interfaces between the fluid phases and of common lines where three phases come in contact. Despite this fact, mathematical descriptions of these flows have been lacking in rigor, consisting primarily of heuristic extensions of Darcy's law that include a hysteretic relation between capillary pressure and saturation and a relative permeability coefficient. As a result, the standard capillary pressure concept appears to have physically unrealistic properties. The present paper employs microscopic mass and momentum balance equations for phases and interfaces to develop an understanding of capillary pressure at the microscale. Next, the standard theories and approaches that define capillary pressure at the macroscale are described and their shortcomings are discussed. Finally, an approach is presented whereby capillary pressure is shown to be an intrinsic property of the system under study. In particular, the presence of interfaces and their distribution within a multiphase system are shown to be essential to describing the state of the system. A thermodynamic approach to the definition of capillary pressure provides a theoretically sound alternative to the definition of capillary pressure as a simple hysteretic function of saturation.

The Effect of streambed topography on surface-subsurface water exchange in mountain catchments

Abstract: A numerical hydrological simulation suggested that water exchange between stream channels and adjacent aquifers is enhanced by convexities and concavities in streambed topography. At St. Kevin Gulch, an effluent stream in the Rocky Mountains of Colorado, subsurface hydraulic gradients and movement of ionic tracers indicated that stream water was locally recharged into well-defined flow paths through the alluvium. Stream water-filled flow paths in the alluvium (referred to as substream flow paths) returned to the stream a short distance downstream (1 to 10 m). Recharge to the substream flow paths occurred where stream water slope increased, at the transition from pools (<1%) to steeper channel units (5–20%). Return of substream flow paths to the stream occurred where stream water slope decreased, at the transition from steeper channel units to pools. A net water flux calculation is typically used to characterize water and solute fluxes between surface and subsurface zones of catchments. Along our study reach at St. Kevin Gulch the net inflow of water from subsurface to stream (1.6 mL s−1 m−1) underestimated the gross inflow (2.7 mL s−1 m−1) by 40%. The influence of streambed topography is to enhance hydrological fluxes between stream water and subsurface zones and to prolong water-sediment contact times; these effects could have important consequences for solute transport, retention, and transformation in catchments.

Calibration of rainfall‐runoff models: Application of global optimization to the Sacramento Soil Moisture Accounting Model

Abstract: Conceptual rainfall-runoff models are difficult to calibrate by means of automatic methods; one major reason for this is the inability of conventional procedures to locate the globally optimal set of parameters. This paper investigates the consistency with which two global optimization methods, the shuffled complex evolution (SCE-UA) method (developed by the authors) and the multistart simplex (MSX) method, are able to find the optimal parameter set during calibration of the Sacramento soil moisture accounting model (SAC-SMA) of the National Weather Service River Forecast System (NWSRFS). In the first phase of this study, error-free synthetic data are used to conduct a comparative evaluation of the algorithms under “ideal” conditions. In 10 independent trials of each algorithm in which 13 parameters of the SAC-SMA model were optimized simultaneously, the SCE-UA method achieved a 100% success rate in locating the precise global optimum (i.e., the “true” parameter values) while the MSX method failed in all trials even with more than twice the number of function evaluations. In the second phase, historical data from the Leaf River watershed are used to conduct a comparative evaluation of the algorithms under “real” conditions, using two different estimation criteria, DRMS and HMLE; the SCE-UA algorithm obtained consistently lower function values and more closely grouped parameter estimates, while using one-third fewer function evaluations than the MSX algorithm.

Stream temperature dynamics: Measurements and modeling

Abstract: A numerical model based on a finite difference solution of the unsteady heat advection-dispersion equation is formulated to predict water temperatures in streams at time increments of 1 hour. An energy balance accounts for the effects of air temperature, solar radiation, relative humidity, cloud cover, and wind speed on the net rate of heat exchange through the water surface, and heat conduction between water and streambed. Continuous stream temperature recordings in shallow streams show strong dynamic behavior including diurnal variations of several degrees Celsius which are lost in the standard daily records. These measured water temperatures are used to calibrate the model for the optimum percentages of Sun shading and wind sheltering. Stream exposure to solar radiation is shown to vary from 30 to 100% and wind exposure from 10 to 30% depending on the character of the stream. Values are related to stream width and season because of variable leaf cover of trees on stream banks. After calibration, accuracies of hourly and daily water temperature predictions over periods of several weeks are of the order of 0.2° to 1°C. Solar (shortwave) radiation is shown to be the most important component of the heat flux across the stream water surface, but none of the other components, i.e., long-wave radiation, evaporation, and convection to the atmosphere, are negligible. Conductive heat exchange between the streambed and the water is a significant heat balance component in shallow streams.

The Value of clean water: The public's willingness to pay for boatable, fishable, and swimmable quality water

Abstract: This paper presents the findings of a study designed to determine the national benefits of freshwater pollution control. By using data from a national contingent valuation survey, we estimate the aggregate benefits of meeting the goals of the Clean Water Act. A valuation function is estimated which depicts willingness to pay as a function of water quality, income, and other variables. Several validation checks and tests for specific biases are performed, and the benefit estimates are corrected for missing and invalid responses. The two major policy implications from our work are that the benefits and costs of water pollution control efforts are roughly equal and that many of the new policy actions necessary to ensure that all water bodies reach at least a swimmable quality level will not have positive net benefits.

L moment diagrams should replace product moment diagrams

Abstract: It is well known that product moment ratio estimators of the coefficient of variation Cν, skewness γ, and kurtosis κ exhibit substantial bias and variance for the small (n ≤ 100) samples normally encountered in hydrologic applications. Consequently, L moment ratio estimators, termed L coefficient of variation τ2, L skewness τ3, and L kurtosis τ4 are now advocated because they are nearly unbiased for all underlying distributions. The advantages of L moment ratio estimators over product moment ratio estimators are not limited to small samples. Monte Carlo experiments reveal that product moment estimators of Cν and γ are also remarkably biased for extremely large samples (n ≥ 1000) from highly skewed distributions. A case study using large samples (n ≥ 5000) of average daily streamflow in Massachusetts reveals that conventional moment diagrams based on estimates of product moments Cν, γ, and κ reveal almost no information about the distributional properties of daily streamflow, whereas L moment diagrams based on estimators of τ2, τ3, and τ4 enabled us to discriminate among alternate distributional hypotheses.

Surface-based Fractional Transport Rates: Mobilization Thresholds and Partial Transport of a Sand-gravel Sediment

Abstract: Twenty-eight coupled observations of flow, transport, and bed surface grain size distribution were made in a laboratory flume using a wide range of flows and a sediment with a very poorly sorted, bimodal grain size distribution. These observations permit the transport rates of individual size fractions to be scaled by the proportion of each size immediately available for transport on the bed surface. The key to our observations is the use of a sediment in which each size fraction has been painted a different color, which permits reliable, repeatable, and nondestructive measurement of the bed surface grain size distribution from photographs of the bed surface. At a given flow, the fractional transport rates may be divided into two parts: a finer-grained portion within which fractional transport rates are a function only of their proportion on the bed surface and total transport rate, and a coarser-grained portion for which fractional transport rates also depend on the proportion of individual grains within a fraction that remain essentially immobile throughout the experimental run. We define the latter condition as one of partial transport and observe that the grain size separating partial and fully mobilized transport consistently increases with flow strength. Complete mobilization of a size fraction occurs at roughly twice the shear stress necessary for incipient motion of that fraction. Zones of partial and full mobility are quite distinct when fractional transport rates are scaled by the bed surface grain size distribution, although a region of partial transport is evident when these data and other experimental and field observations are scaled by the bulk grain size distribution of the sediment bed. Critical shear stresses for the incipient motion of individual fractions in our experimental sediment vary over an order of magnitude, a result strongly in contrast to many earlier observations, but consistent with our observations of incipient motion in sediments with bimodal grain size distributions.

The sizes of salmonid spawning gravels

Abstract: The availability of suitably sized spawning gravels limits salmonid (salmon and trout) populations in many streams. The authors compiles published and original size distribution data to determine distinguishing characteristics of spawning gravels and how gravel size varies with size of the spawning fish. Median diameters of 135 size distributions ranged from 5.4 to 78 mm, with 50% falling between 14.5 and 35 mm. All but three spawning gravel size distributions were negatively skewed (on a log-transformed basis), with 50% of the skewness coefficients falling between [minus]0.24 and [minus]0.39. Fewer than 20% of the distributions were bimodal. Although tending to be coarser, spawning gravels had sorting and skewness values similar to other fluvial gravels reported in the literature. The range of gravel sizes used by fish of a given species or length is great, but the relation between fish size and size of gravel can be described by an envelope curve. In general, fish can spawn in gravels with a median diameter up to about 10% of their body length. 53 refs., 8 figs., 2 tabs.

U.S. streamflow patterns in relation to the El Niño/Southern Oscillation

Abstract: The relationship between the El Nino/Southern Oscillation (ENSO) and unimpaired streamflow over the contiguous United States is studied. The extreme phases of the Southern Oscillation have been linked to fairly persistent classes of atmospheric anomalies over the low and middle latitudes at regional and global scales. Of particular interest in this investigation is the identification of regions of land that appear to have strong and consistent ENSO-related streamflow signals. The first harmonic extracted from a 24-month ENSO composite at each station is assumed to be the ENSO-related signal appearing in streamflow anomalies. These regions were identified by the similarity in phase of the harmonic vectors. The vectorial display of these harmonics over a map of the United States provides the areal extents of ENSO influence on streamflow. Coherent and significant streamflow responses to hypothesized ENSO forcing are found in four regions of the United States: the Gulf of Mexico, the Northeast, the North Central, and the Pacific Northwest. Once an ENSO event sets in, a long-range forecasting utility may be available for these regions. The results of this analysis, which are consistent with previous studies on precipitation and temperature, demonstrate the mid-latitude hydrologic response to the tropical ENSO phenomena.

Evaluation of a first-order water transfer term for variably saturated dual-porosity flow models

Abstract: Variably saturated water flow in a dual-porosity medium may be described using two separate flow equations which are coupled by means of a sink source term Γw, to account for the transfer of water between the macropore (or fracture) and soil (or rock) matrix pore systems. In this study we propose a first-order rate expression for Γw, which assumes that water transfer is proportional to the difference in pressure head between the two pore systems. A general expression for the transfer coefficient αw was derived using Laplace transforms of the linearized horizontal flow equation. The value of αw could be related to the size and shape of the matrix blocks (or soil aggregates) and to the hydraulic conductivity Ka of the matrix at the fracture/matrix interface. The transfer term Γw, was evaluated by comparing simulation results with those obtained with equivalent one- and two-dimensional single-porosity flow models. Accurate results were obtained when Ka was evaluated using a simple arithmetic average of the interface conductivities associated with the fracture and matrix pressure heads. Results improved when an empirical scaling coefficient γw was included in αw. A single value of 0.4 for γw was found to be applicable, irrespective of the hydraulic properties or the initial pressure head of the simulated system.

Mean flow and turbulence fields over two‐dimensional bed forms

Abstract: Detailed laser-Doppler velocity and Reynolds stress measurements over fixed two-dimensional bed forms are used to investigate the coupling between the mean flow and turbulence and to examine effects that play a role in producing the bed form instability and finite amplitude stability. The coupling between the mean flow and the turbulence is explored in both a spatially averaged sense, by determining the structure of spatially averaged velocity and Reynolds stress profiles, and a local sense, through computation of eddy viscosities and length scales. The measurements show that there is significant interaction between the internal boundary layer and the overlying wake turbulence produced by separation at the bed form crest. The interaction produces relatively low correlation coefficients in the internal boundary layer, which suggests that using local bottom stress to predict bed load flux may not only be erroneous, it may also disregard the essence of the bed form instability mechanism. The measurements also indicate that topographically induced acceleration over the bed form stoss slope has a more significant effect in damping the turbulence over bed forms than was previously supposed, which is hypothesized to play a role in the stabilization of fully developed bed forms.

Percolation theory and its application to groundwater hydrology

Abstract: The theory of percolation, originally proposed over 30 years ago to describe flow phenomena in porous media, has undergone enormous development in recent years, primarily in the field of physics. The principal advantage of percolation theory is that it provides universal laws which determine the geometrical and physical properties of the system. This survey discusses developments and results in percolation theory to date, and identifies aspects relevant to problems in groundwater hydrology. The methods of percolation theory are discussed, previous applications of the theory to hydrological problems are reviewed, and future directions for study are suggested.

Modeling of Carbon Dioxide Transport and Production in Soil 1. Model Development

Abstract: Knowledge of the CO2 concentration in the unsaturated zone is essential for prediction of solution chemistry in the vadose zone and groundwater recharge as well as for quantifying carbon source/sink terms as part of the global CO2 mass balance. In this paper we present a predictive simulation model, SOILCO2, based on process-oriented relationships. The model includes one-dimensional water flow and multiphase transport of CO2 utilizing the Richards and the convection-dispersion equations, respectively, as well as heat flow and a CO2 production model. The transport of CO2 in the unsaturated zone can occur in both the liquid and gas phases. The gas transport equation accounts for production of CO2 and uptake of CO2 by plant roots associated with root water uptake. The CO2 production model considers both microbial and root respiration which is dependent on water content, temperature, growth, salinity and plant and soil characteristics. Heat flow is included, since some gas transport parameters, partitioning coefficients and production parameters are strongly temperature dependent. The resulting set of partial differential equations is solved numerically using the finite element and finite difference methods.

A numerical dual‐porosity model with semianalytical treatment of fracture/matrix flow

Abstract: A new dual-porosity model is developed for single-phase fluid flow in fractured/porous media. Flow is assumed to take place through the fracture network and between the fractures and matrix blocks. The matrix blocks are treated in a lumped parameter manner, with a single average pressure used for each matrix block. Rather than assuming that fracture/matrix flux is proportional to the difference between the fracture pressure and matrix pressure at each point, as is done in the Warren-Root model, the authors use a nonlinear equation which more accurately models the flux over all time regimes, including both early and late times. This flux equation is compared with analytical solutions for spherical blocks with prescribed pressure variations on their boundaries. The nonlinear flux equation is also used as a source/sink term in the numerical simulator TOUGH. The modified code allows more accurate simulations than the conventional Warren-Root method, with a large savings (about 90%) in computational time compared to methods which explicitly discretize the matrix blocks. 33 refs., 7 figs.

Mass transfer from nonaqueous phase organic liquids in water-saturated porous media

Abstract: Results of dissolution experiments with trapped nonaqueous phase liquids (NAPLs) are modeled by a mass transfer analysis. The model represents the NAPL as isolated spheres that shrink with dissolution and uses a mass transfer coefficient correlation reported in the literature for dissolving spherical solids. The model accounts for the reduced permeability of a region of residual NAPL relative to the permeability of the surrounding clean media that causes the flowing water to partially bypass the residual NAPL. The dissolution experiments with toluene alone and a benzene-toluene mixture were conducted in a water-saturated column of homogeneous glass beads over a range of Darcy velocities from 0.5 to 10 m d(-1). The model could represent the observed effluent concentrations as the NAPL underwent complete dissolution. The changing pressure drop across the column was predicted following an initial period of NAPL reconfiguration. The fitted NAPL sphere diameters of 0.15 to 0.40 cm are consistent with the size of NAPL ganglia observed by others and are the smallest at the largest flow velocity.

Prediction of steady state flow in nonuniform geologic media by conditional moments: Exact nonlocal formalism, effective conductivities, and weak approximation

Abstract: We consider the effect of measuring randomly varying local hydraulic conductivities K(x) on one's ability to predict steady state flow within a bounded domain, driven by random source and boundary functions. More precisely, we consider the prediction of local hydraulic head h(x) and Darcy flux q(x) by means of their unbiased ensemble moments 〈h(x)〉κ and 〈q(x)〉κ conditioned on measurements of K(x). These predictors satisfy a deterministic flow equation in which 〈q(x)〉κ = −κ(x)∇〈h(x)〉κ + rκ(x), where κ(x) is a relatively smooth unbiased estimate of K(x) and rκ(x) is a “residual flux.” We derive a compact integral expression for rκ(x) which is rigorously valid for a broad class of K(x) fields, including fractals. It demonstrates that 〈q(x)〉κ is nonlocal and non-Darcian so that an effective hydraulic conductivity does not generally exist. We show analytically that under uniform mean flow the effective conductivity may be a scalar, a symmetric or a nonsymmetric tensor, or a set of directional scalars which do not form a tensor. We demonstrate numerically that in two-dimensional mean radial flow it may increase from the harmonic mean of K(x) near interior and boundary sources to the geometric mean far from such sources. For cases where rκ(x) can neither be expressed nor approximated by a local expression, we propose a weak (integral) approximation (closure) which appears to work well in media with pronounced heterogeneity and improves as the quantity and quality of K(x) measurements increase. The nonlocal deterministic flow equation can be solved numerically by standard methods; our theory shows clearly how the scale of grid discretization should relate to the scale, quantity, and quality of available data. After providing explicit approximations for the second moments of head and flux prediction errors, we conclude by discussing practical methods to compute κ(x) from noisy measurements of K(x) and to calculate required second moments of the associated estimation errors when K(x) is lognormal.

Comparison of Penman‐Monteith, Shuttleworth‐Wallace, and Modified Priestley‐Taylor Evapotranspiration Models for wildland vegetation in semiarid rangeland

Abstract: Eddy correlation measurements of sensible and latent heat flux are used with measurements of net radiation, soil heat flux, and other micrometeorological variables to develop the Penman-Monteith, Shuttleworth-Wallace, and modified Priestley-Taylor evapotranspiration models for use in a sparsely vegetated, semiarid rangeland. The Penman-Monteith model, a one-component model designed for use with dense crops, is not sufficiently accurate (r2 = 0.56 for hourly data and r2 = 0.60 for daily data). The Shuttleworth-Wallace model, a two-component logical extension of the Penman-Monteith model for use with sparse crops, performs significantly better (r2 = 0.78 for hourly data and r2 = 0.85 for daily data). The modified Priestley-Taylor model, a one-component simplified form of the Penman potential evapotranspiration model, surprisingly performs as well as the Shuttle worth-Wallace model. The rigorous Shuttleworth-Wallace model predicts that about one quarter of the vapor flux to the atmosphere is from bare-soil evaporation. Further, during daylight hours, the small leaves are sinks for sensible heat produced at the hot soil surface.

A fast and exact method for multidimensional gaussian stochastic simulations

Abstract: To generate multidimensional Gaussian random fields over a regular sampling grid, hydrogeologists can call upon essentially two approaches. The first approach covers methods that are exact but computationally expensive, e.g., matrix factorization. The second covers methods that are approximate but that have only modest computational requirements, e.g., the spectral and turning bands methods. In this paper, we present a new approach that is both exact and computationally very efficient. The approach is based on embedding the random field correlation matrix R in a matrix S that has a circulant/block circulant structure. We then construct products of the square root S1/2 with white noise random vectors. Appropriate sub vectors of this product have correlation matrix R, and so are realizations of the desired random field. The only conditions that must be satisfied for the method to be valid are that (1) the mesh of the sampling grid be rectangular, (2) the correlation function be invariant under translation, and (3) the embedding matrix S be nonnegative definite. These conditions are mild and turn out to be satisfied in most practical hydrogeological problems. Implementation of the method requires only knowledge of the desired correlation function. Furthermore, if the sampling grid is a d-dimensional rectangular mesh containing n points in total and the correlation between points on opposite sides of the rectangle is vanishingly small, the computational requirements are only those of a fast Fourier transform (FFT) of a vector of dimension 2dn per realization. Thus the cost of our approach is comparable with that of a spectral method also implemented using the FFT. In summary, the method is simple to understand, easy to implement, and is fast.

Effective water table depth to describe initial conditions prior to storm rainfall in humid regions

Abstract: A physically meaningful technique to determine the effective depth to the water table, as a measure of the initial storage capacity of a basin is developed. The estimation of the initial storage capacity prior to a given flood event is essential to obtain useful results from storm runoff prediction models based on saturation excess overland flow. It is shown how this effective depth to the water table can be related to streamflow measurements at the outlet of the basin. The analysis is based on Boussinesq's standard hydraulic groundwater theory. The main feature of the present formulation is that it allows the estimation of catchment-scale parameters, namely the aquifer hydraulic conductivity and the average depth to the impervious layer. The estimation of these parameters is based on a drought flow analysis which is consistent with the hydraulic groundwater theory used to develop the described technique. This hydraulic theory is found to be applicable for a catchment under humid temperate climatic conditions, namely the Zwalm catchment situated in East-Flanders, Belgium. The results of the proposed analysis are used to estimate the initial conditions in a partial area runoff generation model. It is shown that accurate estimates of total runoff volume are obtained without further calibration of the model.

Eulerian‐Lagrangian Theory of transport in space‐time nonstationary velocity fields: Exact nonlocal formalism by conditional moments and weak approximation

Abstract: A unified Eulerian-Lagrangian theory is presented for the transport of a conservative solute in a random velocity field that satisfies locally ∇ · v(x, t) = f(x, t), where f(x, t) is a random function including sources and/or the time derivative of head Solute concentration satisfies locally the Eulerian equation ∂c(x, t)/∂t + ∇ · J(x, t) = g(x, t), where J(x, t) is advective solute flux and g(x, t) is a random source independent of f(x, t) We consider the prediction of c(x, t) and J(x, t) by means of their unbiased ensemble moments 〈c(x, t)〉ν and 〈J(x, t)〉ν conditioned (as implied by the subscript) on local hydraulic measurements through the use of the latter in obtaining a relatively smooth unbiased estimate ν(x, t) of v(x, t) These predictors satisfy ∂〈c(x, t)〉v/∂t + ∇ · 〈J(x, t)〉ν = 〈g(x, t)〉ν, where 〈J(x, t)〉ν = ν(x, t)〈c(x, t)〉ν + Qν(x, t) and Qν(x, t) is a dispersive flux We show that Qν, is given exactly by three space-time convolution integrals of conditional Lagrangian kernels αν with ∇·Qν, βν with ∇〈c〉ν, and γν with 〈c〉ν for a broad class of v(x, t) fields, including fractals This implies that Qν(x, t) is generally nonlocal and non-Fickian, rendering 〈c(x, t)〉ν non-Gaussian The direct contribution of random variations in f to Qν depends on 〈c〉ν rather than on ∇〈c〉ν, We elucidate the nature of the above kernels; discuss conditions under which the convolution of βν and ∇〈c〉 becomes pseudo-Fickian, with a Lagrangian dispersion tensor similar to that derived in 1921 by Taylor; recall a 1952 result by Batchelor which yields an exact expression for 〈c〉ν at early time; use the latter to conclude that linearizations which predict that 〈c〉ν bifurcates at early time when the probability density function of v is unimodal cannot be correct; propose instead a weak approximation which leads to a nonlinear integro-differential equation for 〈c〉ν due to an instantaneous point source and which improves with the quantity and quality of hydraulic data; demonstrate that the weak approximation is analogous to the “direct interaction” closure of turbulence theory; offer non-Fickian and pseudo-Fickian weak approximations for the second conditional moment of the concentration prediction error; demonstrate that it yields the so-called “two-particle covariance” as a special case; conclude that the (conditional) variance of c does not become infinite merely as a consequence of disregarding local dispersion; and discuss how to estimate explicitly the cumulative release of a contaminant across a “compliance surface” together with the associated estimation error

A multicomponent decomposition of spatial rainfall fields: 1. Segregation of large‐ and small‐scale features using wavelet transforms

Abstract: Issues of scaling characteristics in spatial rainfall have attracted increasing attention over the last decade. Several methods based on simple and multiscaling and multifractal ideas have been proposed and parameter estimation techniques developed for the hypothesized models. Simulations based on these models have realistic resemblance to “generic rainfall fields.” In this research we analyze rainfall data for scaling characteristics without an a priori assumed model. We look at the behavior of rainfall fluctuations obtained at several scales, via orthogonal wavelet transform of the data, to infer the precise nature of scaling exhibited by spatial rainfall. The essential idea behind the analysis is to segregate large-scale (long wavelength) features from small-scale features and study each of them independently. The hypothesis is set forward that rainfall might exhibit scaling in small-scale fluctuations, if at all, and at large scale this behavior will break down to accommodate the effects of external factors affecting the particular rain-producing mechanism. The validity of this hypothesis is examined. In the first of these papers we develop the methodology for the segregation of large- and small-scale features and apply it to a severe spring time midlatitude squall line storm. The second paper (Kumar and Foufoula-Georgiou, this issue) develops a framework for testing the presence and studying the nature of self-similarity in the fluctuations.

Cross‐correlated random field generation with the direct Fourier Transform Method

Abstract: This paper presents a computer algorithm that is capable of cogenerating pairs of three-dimensional, cross-correlated random fields. The algorithm produces random fields of real variables by the inverse Fourier transform of a randomized, discrete three-dimensional spectral representations of the variables. The randomization is done in the spectral domain in a way that preserves the direct power and cross-spectral density structure. Two types of cross spectra were examined. One type specifies a linear relationship between the two fields, which produces the same correlation scales for both variables but different variances. The second cross spectrum is obtained from a specified transfer function and the two power spectra, and it produces fields with different correlation scales. For both models the degree of correlation is specified by the coherency. A delay vector can also be specified to produce an out-of-phase correlation between the two fields. The algorithm is very efficient computationally, is relatively easy to use, and does not produce the lineation problems that can be encountered with the turning bands method. Perhaps most important, this random field generator is capable of co-generating cross-correlated random fields.

Monitoring an underground steam injection process using electrical resistance tomography

Abstract: We used electrical resistance tomography (ERT) to map the subsurface distribution of a steam flood as a function of time as part of a prototype environmental restoration process performed by the Dynamic Underground Stripping Project. We evaluated the capability of ERT to monitor changes in the soil resistivity during the steam injection process using a dipole-dipole measurement technique to measure the bulk electrical resistivity distribution in the soil mass. The injected steam caused changes in the soil's resistivity because the steam displaced some of the native pore water, increased the pore water and soil temperatures and changed the ionic content of the pore water. We could detect the effects of steam invasion by mapping changes in the soil resistivity as a function of space and time. The ERT tomographs are compared with induction well logs, formation temperature logs and lithologic logs. These comparisons suggest that the ERT tomographs mapped the formation regions invaded by the steam flood. The data also suggest that steam invasion was limited in vertical extent to a gravel horizon at depth of approximately 43 m. The tomographs show that with time, the steam invasion zone extended laterally to all areas monitored by the ERT technique.

Multiporosity/multipermeability approach to the simulation of naturally fractured reservoirs

Abstract: This paper presents an array of deformation-dependent flow models of various porosities and permeabilities relevant to the characterization of naturally fractured reservoirs. A unified multiporosity multipermeability formulation is proposed as a generalization of the porosity- or permeability-oriented models of specific degree. Some new relationships are identified in the parametric investigation for both single-porosity and dual-porosity models. A formula is derived to express Skempton's constant B by Biot's coefficient H and relative compressibility ϕ*. It is found that the recovery of the original expression for Skempton's constant B is largely dependent on the choice of ϕ*, representing relative compressibility. The dual-porosity/dual-permeability model is evaluated through an alternative finite element approximation. The deformation-dependent fracture flow mechanism is introduced where the rock matrix possesses low permeability and fracture flow is dominant. A preliminary study of the reservoir simulation identifies the strong coupling between the fluid flow and solid deformation.

Field Experiments in a Fractured Clay Till 2. Solute and Colloid Transport

Abstract: A field tracer experiment was conducted in a lateral flow field in the weathered and highly fractured upper 6 m of a 40-m-thick clay-rich till plain in southwestern Ontario. In the upper 3 m where fractures are closely spaced ( 5 m/d. Simulations with a discrete fracture/porous matrix flow and transport model, which used the cubic law for flow in fractures, showed that diffusion of the solutes, but not the much larger colloids, into the matrix pore water between fractures is sufficient to cause the observed difference in solute and colloid transport rates. Transport-derived and hydraulic conductivity-derived fracture aperture values were similar, within a factor of 3 and falling mainly within a range of 5–40 μm. In the upper 3 m the solute tracers were evenly distributed between pore water in the fractures and the matrix, and as a result, solute transport can be closely approximated with an equivalent porous medium (EPM) approach. Below this depth, fractures are more widely spaced (0.13 to >1 m) with concentration peaks tending to occur near visible fractures, and solute transport cannot be adequately described with an EPM approach.