Showing papers in "Water Resources Research in 1984"

A Nonparametric Trend Test for Seasonal Data With Serial Dependence

Abstract: Statistical tests for monotonic trend in seasonal (e.g., monthly) hydrologic time series are commonly confounded by some of the following problems: nonnormal data, missing values, seasonality, censoring (detection limits), and serial dependence. An extension of the Mann-Kendall test for trend (designed for such data) is presented here. Because the test is based entirely on ranks, it is robust against nonnormality and censoring. Seasonality and missing values present no theoretical or computational obstacles to its application. Monte Carlo experiments show that, in terms of type I error, it is robust against serial correlation except when the data have strong long-term persistence (e.g., ARMA (1, 1) monthly processes with ϕ > 0.6) or short records (∼ 5 years). When there is no serial correlation, it is less powerful than a related simpler test which is not robust against serial correlation.

A Statistical Exploration of the Relationships of Soil Moisture Characteristics to the Physical Properties of Soils

Abstract: Stochastic modeling of soil water fluxes in the absence of measured hydraulic parameters requires a knowledge of the expected distribution of the hydraulic parameters in different soil types. Predictive relationships describing the hydraulic parameter distributions must be developed based on the common descriptors of the physical properties of soils (e.g., texture, structure, particle size distribution). Covariation among the hydraulic parameters within these relationships must be identified. Data for 1448 soil samples were examined in an evaluation of the usefulness of qualitative descriptors as predictors of soil hydraulic behavior. Analysis of variance and multiple linear regression techniques were used to derive quantitative expressions for the moments of the hydraulic parameters as functions of the particle size distributions (percent sand, silt, and clay content) of soils. Discriminant analysis suggests that the covariation of the hydraulic parameters can be used to construct a classification scheme based on the hydraulic behavior of soils that is analogous to the textural classification scheme based on the sand, silt, and clay content of soils.

Modeling persistence in hydrological time series using fractional differencing

Abstract: The class of autoregressive integrated moving average (ARIMA) time series models may be generalized by permitting the degree of differencing d to take fractional values. Models including fractional differencing are capable of representing persistent series (d > 0) or short-memory series (d = 0). The class of fractionally differenced ARIMA processes provides a more flexible way than has hitherto been available of simultaneously modeling the long-term and short-term behavior of a time series. In this paper some fundamental properties of fractionally differenced ARIMA processes are presented. Methods of simulating these processes are described. Estimation of the parameters of fractionally differenced ARIMA models is discussed, and an approximate maximum likelihood method is proposed. The methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures.

Sediment Production From Forest Road Surfaces

Abstract: Erosion on roads is an important source of fine-grained sediment in streams draining logged basins of the Pacific Northwest. Runoff rates and sediment concentrations from 10 road segments subject to a variety of traffic levels were monitored to produce sediment rating curves and unit hydrographs for different use levels and types of surfaces. These relationships are combined with a continuous rainfall record to calculate mean annual sediment yields from road segments of each use level. A heavily used road segment in the field area contributes 130 times as much sediment as an abandoned road. A paved road segment, along which cut slopes and ditches are the only sources of sediment, yields less than 1% as much sediment as a heavily used road with a gravel surface.

Two-Component Extreme Value Distribution for Flood Frequency Analysis

Abstract: Theoretical considerations, supported by statistical analysis of 39 annual flood series (AFS) of Italian basins, suggest that the two-component extreme value (TCEV) distribution can be assumed as a parent flood distribution, i.e., one closely representative of the real flood experience. This distribution belongs to the family of distributions of the annual maximum of a compound Poisson process, which is a solid theoretical basis for AFS analysis. However, the two-parameter distribution of this family, obtained on the assumption of identically distributed floods, does not account for the high variability of both observed skewness and largest order statistics, so that a significant number of observed floods qualify as outliers under this distribution. The more general TCEV distribution assumes individual floods to arise from a mixture of two exponential components. Its four parameters can be estimated by the maximum likelihood method. A regionalized TCEV distribution, with parameters representative of a set of 39 Italian AFS's, was shown to closely reproduce the observed distribution of skewness and that of the largest order statistic.

Nonparametric Tests for Trend in Water Quality

Abstract: Recently, several nonparametric tests for trends in water quality have been proposed. These tests have been developed because the assumptions of classical parametric methods (i.e., normality, linearity, independence) are usually not met by typical water quality data. Additional idiosyncrasies of the data, such as missing values, censored data, and seasonality, compound the analysis problem. The nonparametric methods are more flexible and can handle these problems more easily. However, information on relative power of the various nonparametric procedures has not been reported in the hydrologic literature. For this reason, two classes of procedures, intrablock methods (procedures that compute a statistic, such as Kendall's tau, for each block or season and then sum these to produce a single overall statistic), and aligned rank methods (procedures that remove the block effect from each datum, sum the data over blocks, and then create a statistic from these sums) are examined in detail. Results from the statistical literature show that aligned rank methods are asymptotically more powerful than intrablock methods. In contrast, intrablock methods are more adaptable. Procedures to analyze more general models, including multistation designs and models, which include a trend-season or trend-site interaction, are developed by using Kendall's tau and intrablock methods. Finally, some recommendations on the analysis of data sets with missing values and multiple values per season values are presented.

Double‐Porosity Models for a Fissured Groundwater Reservoir With Fracture Skin

Abstract: Theories of flow to a well in a double-porosity groundwater reservoir are modified to incorporate effects of a thin layer of low-permeability material or fracture skin that may be present at fracture-block interfaces as a result of mineral deposition or alteration. The commonly used theory for flow in double- porosity formations that is based upon the assumption of pseudo–steady state block-to-fissure flow is shown to be a special case of the theory presented in this paper. The latter is based on the assumption of transient block-to-fissure flow with fracture skin. Under conditions where fracture skin has a hydraulic conductivity that is less than that of the matrix rock, it may be assumed to impede the interchange of fluid between the fissures and blocks. Resistance to flow at fracture-block interfaces tends to reduce spatial variation of hydraulic head gradients within the blocks. This provides theoretical justification for neglecting the divergence of flow in the blocks as required by the pseudo–steady state flow model. Coupled boundary value problems for flow to a well discharging at a constant rate were solved in the Laplace domain. Both slab-shaped and sphere-shaped blocks were considered, as were effects of well bore storage and well bore skin. Results obtained by numerical inversion were used to construct dimensionless-type curves that were applied to well test data, for a pumped well and for an observation well, from the fractured volcanic rock terrane of the Nevada Test Site.

Stochastic dynamic programming models for reservoir operation optimization

Abstract: Most applications of stochastic dynamic programming have derived stationary policies which use the previous period's inflow as a hydrologic state variable. This paper develops a stochastic dynamic programming model which employs the best forecast of the current period's inflow to define a reservoir release policy and to calculate the expected benefits from future operations. Use of the best inflow forecast as a hydrologic state variable, instead of the preceding period's inflow, resulted in substantial improvements in simulated reservoir operations with derived stationary reservoir operating policies. While these results are for a dam at Aswan in the Nile River Basin, operators of other reservoir systems also have available to them information other than the preceding period's inflow which can be used to develop improved inflow forecasts.

On the Equivalence of Two Conceptual Models for Describing Ion Exchange During Transport Through an Aggregated Oxisol

Abstract: Breakthrough curves (BTCs) of the cation 45Ca2+, an anion 36Cl−, and 3H2O were measured during miscible displacement through water-saturated soil columns packed with aggregates of an Oxisol. Two conceptual models were used to simulate the observed asymmetry and tailing in the BTCs caused by an apparent nonequilibrium situation in the porous medium. In both models the exchange process on one type of site was assumed to be instantaneous while the rate of isotopic exchange on another type of site was assumed to be either a diffusion-controlled process (model 1) or a first-order reversible kinetic process (model 2). Isotopic exchange in both models was described with a linear isotherm. It is shown that the two models are mathematically equivalent with respect to the derived BTCs.

An Application of the Geostatistical Approach to the Inverse Problem in Two-Dimensional Groundwater Modeling

Abstract: The geostatistical approach to the estimation of transmissivity from head and transmissivity measurements is developed for two-dimensional steady flow. The field of the logarithm of transmissivity (log-transmissivity) is represented as a zero-order intrinsic random field; its spatial structure is described in this application through a two-term covariance function that is linear in the parameters θ1 and θ2. Linearization of the discretized flow equations allows the construction of the joint covariance matrix of the head and log transmissivity measurements as a linear function of θ1 and θ2. In this particular application the coefficient matrices are calculated numerically in a noniterative fashion. Maximum likelihood estimation is employed to estimate θ1 and θ2 as well as additional parameters from measurements. Linear estimation theory (cokriging) then yields point or block-averaged estimates of transmissivity. The approach is first applied to a test case with favorable results. It is shown that the application of the methodology gives good estimates of transmissivities. It is also shown that when the transmissivities are used in a numerical model they reproduce the head measurements quite well. Results from the application of the methodology to the Jordan aquifer in Iowa are also presented.

The Effect of Tortuosity on Fluid Flow Through a Single Fracture

Abstract: Calculations to investigate the effect of path tortuosity and connectivity on fluid flow rate through a single rough fracture were carried out. The flow paths are represented by electrical resistors placed on a two-dimensional grid, and the resistances vary as the inverse of the fracture aperture cubed. The electric current through the circuit bears a one-to-one correspondence to the fluid flow rate. Both fracture apertures derived from measurements and from hypothetical analytic functions were used in a parameter study to investigate the dependence of tortuosity on fracture roughness characteristics. It was found that the more small apertures there are in the aperture distribution, the larger is the effect of tortuosity. When the fraction of contact area between the fracture surfaces rises above 30%, the aperture distributions are invariably large at small apertures, and the effect of fracture roughness and flow path tortuosity depresses flow rate from the value predicted by the parallel plate representation of a fracture by three or more orders of magnitude. The impact of these results on the calculations and measurements in fracture hydrology is discussed.

Channel Networks: A Geomorphological Perspective

Abstract: The study of channel networks has been dominated since 1966 by the random model However, recent work has shown (1) that although the topological properties of small networks conform to the random model more closely than those of large ones, even small networks exhibit systematic deviations from topological randomness and (2) that the topological and length properties of channel networks are controlled to a large degree by the spatial requirements of subbasins and the need for these subbasins to fit together in space, by the size, sinuosity, and migration rate of valley bends, and by the length and steepness of valley sides The factors that control the density properties of channel networks vary with the scale of the investigation and the geomorphic processes governing channel initiation Although progress has been made toward a satisfactory stream junction angle model, further work is needed The evolution of channel networks has been investigated by a variety of methods, including the development of conceptual and simulation models, the monitoring of small-scale badland and experimental drainage basins, and the substitution of space for time The morphology of most channel networks is largely inherited from the past or strongly influenced by inherited forms Inasmuch as there is no way of ever knowing the origin or complex history of such networks, the use of stochastic models in their study seems unavoidable

On the Treatment of Evapotranspiration, Soil Moisture Accounting, and Aquifer Recharge in Monthly Water Balance Models

Abstract: Several two- to six-parameter regional water balance models are examined by using 50-year records of monthly streamflow at 10 sites in New Jersey. These models include variants of the Thornthwaite-Mather model, the Palmer model, and the more recent Thomas abcd model. Prediction errors are relatively similar among the models. However, simulated values of state variables such as soil moisture storage differ substantially among the models, and fitted parameter values for different models sometimes indicated an entirely different type of basin response to precipitation. Some problems in parameter identification are noted, including difficulties in identifying an appropriate time lag factor for the Thornthwaite-Mather-type model for basins with little groundwater storage, very high correlations between upper and lower storages in the Palmer-type model, and large sensitivity of parameter a of the abcd model to bias in estimates of precipitation and potential evapotranspiration. Modifications to the threshold concept of the Thornthwaite-Mather model were statistically valid for the six stations in northern New Jersey. The abcd model resulted in a simulated seasonal cycle of groundwater levels similar to fluctuations observed in nearby wells but with greater persistence. These results suggest that extreme caution should be used in attaching physical significance to model parameters and in using the state variables of the models in indices of drought and basin productivity.

Modeling subsurface stormflow on steeply sloping forested watersheds

Abstract: Five mathematical models for predicting subsurface flow were compared to discharge measurements made by Hewlett and Hibbert (1963) on a uniform sloping soil trough at the Coweeta Hydrologic Laboratory. The models included one- and two-dimensional finite element models based on the Richards equation, a kinematic wave model, and two simple storage-discharge models based on the kinematic wave and Boussinesq assumptions. The simple models simulated the subsurface response and water table positions as well as the more complex models based on the Richards equation and were much more economical to use from the point of view of computational costs. Such models have features that would allow them to be incorporated into more complex watershed models, thus placing hydrologic prediction on a more physically correct and less empirical footing.

Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined With Nonlinear Programing

Abstract: A simulation-management methodology is demonstrated for the rehabilitation of aquifers that have been subjected to chemical contamination. Finite element groundwater flow and contaminant transport simulation are combined with nonlinear optimization. The model is capable of determining well locations plus pumping and injection rates for groundwater quality control. Examples demonstrate linear or nonlinear objective functions subject to linear and nonlinear simulation and water management constraints. Restrictions can be placed on hydraulic heads, stresses, and gradients, in addition to contaminant concentrations and fluxes. These restrictions can be distributed over space and time. Three design strategies are demonstrated for an aquifer that is polluted by a constant contaminant source: they are pumping for contaminant removal, water injection for in-ground dilution, and a pumping, treatment, and injection cycle. A transient model designs either contaminant plume interception or in-ground dilution so that water quality standards are met. The method is not limited to these cases. It is generally applicable to the optimization of many types of distributed parameter systems.

Bed Load Transport in a River Meander

Abstract: Bed load transport in Muddy Creek, Wyoming, a sand-bedded meandering river with equilibrium bottom topography, was found to consist of a zone of maximum sediment flux that shifted across the channel from near the inside bank in the upstream part of the bend toward the pool at the minimum radius of curvature. Significant net cross-stream transport continued even through the crossings between the bends. The downstream bed load transport field for the bend which was studied in greatest detail was the same as that computed from bed form migration measurements and can be predicted from appropriate boundary shear stress data and the Yalin bed load equation. The zone of maximum bed load transport followed an outward-shifting region of maximum boundary shear stress, although in the downstream end of the bend the sediment transport maximum tended to stay closer to the centerline than the boundary shear stress maximum due to particle size influences. Net cross-stream transport varied with particle size and was effected by three major processes: topographically-induced, near-bed, cross-stream flow; trough wise flow along obliquely oriented bed forms; and rolling or avalanching of particles on bed form lee faces plus rolling or mass sliding on a steep cross-stream point bar side slope. Coarse particles were carried outward over the top of the point bar by a near-bed cross-stream flow that was induced by downstream shoaling. These particles then rolled and slid on the point bar side slope and eventually were carried toward the outer bank by troughwise transport along oblique dunes. In the upstream part of the bend, fine particles were carried inward by the channel curvature-induced, near-bed flow and by troughwise transport along lee faces of oblique bed forms. Fine particles and coarse particles crossed paths on top of the point bar, where weak troughwise flow moved just the finer particles toward the convex bank, and on the point bar face, where coarse particles rolled against the secondary circu- lation that was carrying the finer particles. Net cross-stream bed load transport was toward the pool and was on average about 10% of the downstream bed load transport. The Engelund equation predicts reasonably well the general pattern of net cross-stream transport through the meander, but it does not account for the substantial troughwise transport caused by oblique bedforms at several locations in the bend. Our observations suggest that equilibrium bed topography occurs when there is net outward transport into the outward shifting zone of maximum boundary shear stress.

Managing Water Scarcity: An Evaluation of Interregional Transfers

Abstract: An interregional trade model is developed for assessing the potential of limited market institutions to alleviate water scarcity. The model differs from those of Takayama and Judge, since curvilinear demand functions are employed and an unequal number of supply and demand regions are specified. The model is applied to California using regional supply and demand functions estimated for 1980, 1995, and 2020. The results show that water transfers can be substituted for new supplies to the extent that less than 100,000 ac ft (123 × 106 m3) of new capacity could be justified by 2020. The net benefits to buyers and sellers total $66 million for 1980 and rise to $219 million by 2020. The work also demonstrates that trade would lead to premature drawdown of groundwater resources in the absence of management and might create excess supply capacity for urban regions.

A Spectral Theory of Rainfall Intensity at the Meso-β Scale

Abstract: The available empirical descriptions of extratropical cyclonic storms are employed to formulate a physically realistic stochastic representation of the ground level rainfall intensity field in space and time. The stochastic representation is based on three-component stochastic point processes which possess the general features of the embedding of rain cells within small mesoscale areas within large mesoscale areas within synoptic storms. Certain scale idealizations, and assumptions on functional forms which qualitatively reflect the physical features, lead to a closed form expression for the covariance function, i.e., the real space-time spectrum, of the rainfall intensity field. The theoretical spectrum explains the empirical spectral features observed by Zawadzki almost a decade ago. Of particular interest and importance in this connection is an explanation of the empirical observation that the Taylorian propogation of the fine scale structure, via a transformation of time to space through the storm velocity, holds only for a small time lag and not throughout. The results here indicate the extent of this lag in terms of the characteristic scales associated with cell durations, cellular birthrates and velocities, etc.

On the Problem of Permissible Covariance and Variogram Models

Abstract: The covariance and variogram models (ordinary or generalized) are important statistical tools used in various estimation and simulation techniques which have been recently applied to diverse hydrologic problems. For example, the efficacy of kriging, a method for interpolating, filtering, or averaging spatial phenomena, depends, to a large extent, on the covariance or variogram model chosen. The aim of this article is to provide the users of these techniques with convenient criteria that may help them to judge whether a function which arises in a particular problem, and is not included among the known covariance or variogram models, is permissible as such a model. This is done by investigating the properties of the candidate model in both the space and frequency domains. In the present article this investigation covers stationary random functions as well as intrinsic random functions (i.e., nonstationary functions for which increments of some order are stationary). Then, based on the theoretical results obtained, a procedure is outlined and successfully applied to a number of candidate models. In order to give to this procedure a more practical context, we employ “stereological” equations that essentially transfer the investigations to one-dimensional space, together with approximations in terms of polygonal functions and Fourier-Bessel series expansions. There are many benefits and applications of such a procedure. Polygonal models can be fit arbitrarily closely to the data. Also, the approximation of a particular model in the frequency domain by a Fourier-Bessel series expansion can be very effective. This is shown by theory and by example.

Wetting front advance and freezing of meltwater within a snow cover: 1. Observations in the Canadian Arctic

Abstract: In a naturally stratified snow cover the movement of meltwater into dry snow is complicated by the interaction of the wetting front with stratigraphic horizons. Field observations showed that when the wetting front reached premelt stratigraphic horizons, water ponded at the interface and then flow fingers developed and penetrated the lower stratum. The flux in these fingers, which was increased to about twice that of the surface flux, was used to feed water to the impeding horizons where it froze to form ice layers. These ice layers were the major source of latent heat released within the snow cover, and they were responsible for the warming of the snow and the underlying soil. These continuous ice layers grew only at stratigraphic boundaries. Because of this ice layer growth the wetting front advance was retarded, and the arrival of meltwater at the snow cover base was significantly delayed. Owing to a cold substrate the strong heat flux from the snow into the soil delays the warming of the snow cover and limits runoff after the snow is isothermal at 0°C by the refreezing of soil infiltration and the development of a basal ice layer.

Sufficient conditions for river meandering: A simulation approach

Abstract: A digital simulation model produces realistic meandering patterns starting from an initially straight channel with small random perturbations. The model assumes that nominal migration rates increase as channel curvature increases but reach a maximum when bend radius divided by channel width is about 3, with decreasing rates for sharper bends, in accord with observations of Nanson and Hickin (1983) and others. However, it is also necessary to assume that local migration rates are a weighted average of local and upstream nominal rates, with the weighting decreasing upstream. The model includes provisions for neck cutoffs and may be used to forecast future patterns of channel migration in meandering streams.

Nash Model Relation to Horton Order Ratios

Abstract: The Nash model of the instantaneous unit hydrograph (IUH) is parameterized in terms of Horton order ratios of a catchment on the basis of a geomorphologic model of catchment response. The shape parameter of the Nash model is found to depend on Horton's numbers RA, RB, and RL of a catchment; thus catchment geomorphology can provide a synthesis of the shape of the hydrologic response. The scale parameter of the Nash model results to be a time-varying character depending on both geomorphology and average streamflow velocity along the stream network; thus the time scale of the IUH could account for the variability of the hydrologic response for different storms and throughout a storm.

Scale considerations in the modeling of temporal rainfall

Abstract: Observations on temporal rainfall are invariably taken in cumulative amounts over disjoint intervals representing different time scales such as hours, days, etc. At these scales a mathematical description of the rainfall process is shown to depend on the scale of measurements. This illustration is carried out employing three stochastic models having different dependence structures which range from complete independence and Markovian dependence to non-Markovian clustering dependence. The problem of estimating the model parameters is also shown to be tied to the scale of measurements. Hourly and daily rainfall data from Denver, Colorado, and daily rainfall data from Agua Fria, Venezuela, are employed for this illustration.

Solute Transfer Through Columns of Glass Beads

Abstract: Miscible displacement experiments were conducted in a 30-cm-long column filled with glass beads that had diameters in the range of 74–125 µm. Breakthrough curves were determined at various leaching rates for saturated or unsaturated conditions. The breakthrough curves of the unsaturated experiments showed early breakthrough and tailing. These could be described with the classical dispersion equation, provided dispersion coefficients were used, which were about 20 times larger than for saturated columns leached at comparable pore water velocities. A better description of these breakthrough curves was obtained with a model accounting for mobile and immobile water. With this model the dispersion coefficients, as obtained from the saturated experiments, could be used directly. The immobile water content was found to increase linearly with the total water content, while the transfer coefficient for solute transport into the immobile water increased proportionally with the pore water velocity. It is shown, based on the mobile and immobile water and solute transport model, that breakthrough curves of long unsaturated columns should exhibit no early breakthrough and tailing but that the presence of immobile water will result in predictably larger dispersion coefficients than those expected on the basis of saturated flow experiments alone.

Techniques for Making Finite Elements Competitve in Modeling Flow in Variably Saturated Porous Media

Abstract: A Galerkin finite element formulation is developed for the numerical simulation of water flow in variably saturated soil systems. Included in this formulation is a solution strategy based on Picard and Newton-Raphson algorithms. Both algorithms are designed especially to cope with severely nonlinear field problems. The two algorithms are formulated for both rectangular and triangular elements. The element matrices are evaluated in a simple and efficient manner using a technique referred to as the “influence coefficient” technique. This technique avoids numerical integration and leads to a substantial saving of computational cost. Four examples are presented to demonstrate the effectiveness of the present finite element approach. These examples show that the nonlinear solution schemes are capable of accomodating cases involving large variations in the saturated hydraulic conductivity, as well as highly nonlinear soil moisture characteristics. A comparative study of the Picard and the Newton-Raphson algorithms is also provided. The study indicates that despite the higher cost per iteration of the Newton-Raphson scheme, it usually requires a substantially smaller number of iterations than the Picard scheme. In some instances where convergence difficulties are experienced with the latter scheme, it is desirable to use the Newton-Raphson scheme in order to obtain a cost-effective solution to the problem.

The Operational Significance of the Continuum Hypothesis in the Theory of Water Movement Through Soils and Aquifers

Abstract: The operational meaning of the representative elementary volume (REV) concept, on which current foundational theories of water movement through porous media are based, is analyzed critically. It is concluded that the REV concept as applied to real porous media is both unnecessarily restrictive and experimentally unverifiable. In its place a relativist concept is proposed in which macroscopic physical variables are defined as convolution products of microscopic properties of a porous medium with weighting functions that represent the appropriate measuring instruments. The effects of resolution and precision differences among experimental measuring devices, now recognized as critical in the assessment of spatial variability in the properties of soils and aquifers, can be incorporated naturally within the relativist concept but are excluded a priori in the REV concept. The relativist point of view, unlike the REV concept, has a clear operational meaning and, in principle, extends theoretical validity to all local measurements made on porous media. It is sufficient mathematically to derive conventional macroscopic balance equations for mass and linear momentum as well as a differential equation for the isothermal transport of water through an unsaturated, anisotropic, deformable soil or aquifer.

A Model for Flow in Meandering Streams

Abstract: Erosion and deposition in streams and tidal channels depend on the divergence of the sediment-flux field, and this is governed by the distribution of boundary shear stress. As a consequence, erosion arid deposition patterns in such systems are sensitive to spatial variations in boundary shear stress, which in turn, can be induced by the complex interplay between the flow and bed and bank topography. A method whereby variations in boundary shear stress can be calculated is presented herein for flows that are broad in relation to their depth and for which the bed slopes are small. The formal scheme employs a regular perturbation expansion around a zero-order state that includes vertically integrated, topographically induced convective accelerations. Use of a zero-order velocity field that includes these accelerative effects yields a model that is applicable to streams with typical bed slopes and channel curvatures, one that can be employed in the majority of situations of interest to geomorphologists, sedimentologists, and hydraulic engineers concerned with fluvial and estuarine systems. In order to verify the model, our calculations are shown to reproduce, with reasonable accuracy, the free-surface topography and boundary shear stress distribution measured by Hooke (1975) when applied to a channel of the geometry that he investigated. The latter part of the paper describes how the interplay of the various components of flow through a curved channel with bar-pool topography is affected by the parameters of the problem.

A Simulation Analysis of Thermal Effects on Evaporation From Soil

Abstract: The Richards equation, which expresses the conservation of water in an isothermal soil, has a more general form in a nonisothermal soil. In using the latter, it is necessary to know soil temperature, and modeling becomes considerably more complicated. A detailed, numerical simulation model quantifies the thermal effects for two hypothetical soils under two climates. During characteristic 4-day climatic sequences, in a season of soil heating, diffusion of vapor due to thermally induced vapor concentration gradients suppresses evaporation. The suppression is greatest (5–15% in this set of experiments) under arid conditions. Under these conditions, such thermal vapor diffusion also distorts the usual diurnal pattern of evaporation. Evaporation is generally more sensitive to isothermal than to thermal vapor diffusion. Variations in time and depth of the soil temperature cause corresponding variations in the water transport coefficients. These, in turn, result in biases (2–5%) and diurnal distortions of evaporation rates. Liquid flow attributable to the dependence of matric potential on temperature accounts for about 1% of evaporation in our experiments. In simulations of 1 month duration for each combination of soil and climate, the joint neglect of all thermal effects mentioned above introduces an error of only about 1% in the average evaporation rate and does not distort its time distribution significantly.

An Analysis of the Influence of Fracture Geometry on Mass Transport in Fractured Media

Abstract: A stochastic modeling technique has been developed to investigate mass transport within a network of discrete fractures. The fracture network is composed of two orthogonal fracture sets, with fracture length, location, and aperture characterized by appropriate probability distributions. Emphasis is placed on understanding how fracture geometry influences mass transport within a network of discontinuous fractures. The network is aligned in such a manner that one fracture set (set one) forms the dominant pathway for transport. The primary role of the second fracture set is to provide connecting pathways between the discontinuous fractures of set one. Results suggest that mass transport can be described in terms of the directness of the connection between the upstream and downstream boundaries. Variations in fracture geometry which have the effect of increasing the probability that a relatively indirect or circuitous pathway exists through the network generally lead to an increase in both the mean and the standard deviation in the arrival time of various breakthrough fractions. Examples include a reduction in the number of fractures forming the set aligned with the direction of the hydraulic gradient or a decrease in the average length of fractures forming that set. Variations in fracture geometry which have the effect of increasing the probability that a relatively direct pathway will exist through the network have the opposite effect. Transport is sensitive to the variability in fracture aperture. The connectivity of the fracture network is also shown to influence the magnitude of dispersive effects.