Showing papers in "Water Resources Research in 1982"

Macropores and water flow in soils

Abstract: This paper reviews the importance of large continuous openings (macropores) on water flow in soils. The presence of macropores may lead to spatial concentrations of water flow through unsaturated soil that will not be described well by a Darcy approach to flow through porous media. This has important implications for the rapid movement of solutes and pollutants through soils. Difficulties in defining what constitutes a macropore and the limitations of current nomenclature are reviewed. The influence of macropores on infiltration and subsurface storm flow is discussed on the basis of both experimental evidence and theoretical studies. The limitations of models that treat macropores and matrix porosity as separate flow domains is stressed. Little-understood areas are discussed as promising lines for future research. In particular, there is a need for a coherent theory of flow through structured soils that would make the macropore domain concept redundant.

Techniques of trend analysis for monthly water quality data

Abstract: Some of the characteristics that complicate the analysis of water quality time series are non-normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as ‘less than’: the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow-adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow-adjusted concentrations, which may also be seasonal and non-normal, can then be tested for trend by using the seasonal Kendall test.

Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation

Abstract: Three criteria for evaluating the possible performance of water resource systems are discussed. These measures describe how likely a system is to fail (reliability), how quickly it recovers from failure (resiliency), and how severe the consequences of failure may be (vulnerability). These criteria can be used to assist in the evaluation and selection of alternative design and operating policies for a wide variety of water resource projects. The performance of a water supply reservoir with a variety of operating policies illustrates their use.

Porous media equivalents for networks of discontinuous fractures

Abstract: The theory of flow through fractured rock and homogeneous anisotropic porous media is used to determine when a fractured rock behaves as a continuum. A fractured rock can be said to behave like an equivalent porous medium when (1) there is an insignificant change in the value of the equivalent permeability with a small addition or subtraction to the test volume and (2) an equivalent permeability tensor exists which predicts the correct flux when the direction of a constant gradient is changed. Field studies of fracture geometry are reviewed and a realistic, two-dimensional fracture system model is developed. The shape, size, orientation, and location of fractures in an impermeable matrix are random variables in the model. These variables are randomly distributed according to field data currently available in the literature. The fracture system models are subjected to simulated flow tests. The results of the flow tests are plotted as permeability ‘ellipses.’ The size and shape of these permeability ellipses show that fractured rock does not always behave as a homogeneous, anisotropic porous medium with a symmetric permeability tensor. Fracture systems behave more like porous media when (1) fracture density is increased, (2) apertures are constant rather than distributed, (3) orientations are distributed rather than constant, and (4) larger sample sizes are tested. Preliminary results indicate the use of this new tool, when perfected, will greatly enhance our ability to analyze field data on fractured rock systems. The tool can be used to distinguish between fractured systems which can be treated as porous media and fractured systems which must be treated as a collection of discrete fracture flow paths.

Settling velocity of natural particles

Abstract: Data from 14 previous experimental studies were used to develop an empirical equation that accounts for the effects of size, density, shape, and roundness on the settling velocity of natural sediment. This analysis was done in terms of four nondimensional parameters, namely, the dimensionless nominal diameter D*, the dimensionless settling velocity W*, the Corey shape factor, and the Powers roundness index. For high D* (large or dense particles), changes in roundness and shape factor have similar magnitude effects on settling velocity. Roundness varies much less for naturally occuring grains, however, and hence is a less important control than shape. For a typical coarse sand with a Powers roundness of 3.5 and a Corey shape factor of 0.7, the settling velocity is about 0.68 that of a sphere of the same D*, with shape and roundness effects contributing about equally to the settling velocity reduction. At low D* the reduction in settling velocity due to either shape or roundness is much less. Moreover, at low D*, low roundness causes a greater decrease in settling velocity at low shape factor values than at high shape factor values. This appears to be due to the increased surface drag on the flatter grains.

Contaminant transport in fractured porous media: Analytical solutions for a system of parallel fractures

Abstract: An exact analytical solution is developed for the problem of transient contaminant transport in discrete parallel fractures situated in a porous rock matrix. The solution takes into account advective transport in the fractures, molecular diffusion and mechanical dispersion along the fracture axes, molecular diffusion from the fracture to the porous matrix, adsorption onto the face of the matrix, adsorption within the matrix, and radioactive decay. The general transient solution is in the form of a double integral that is evaluated using Gauss-Legendre quadrature. A transient solution is also presented for the simpler problem that assumes negligible longitudinal dispersion along the fracture. This assumption is usually reasonable when the advective flux in a fracture is large. A comparison between two steady state solutions, one with dispersion and one without, permits a criterion to be developed that is useful for assessing the significance of longitudinal dispersion in terms of the overall system response. Examples of the solutions demonstrate that penetration distances along fractures can be substantially larger through multiple, closely spaced fractures than through a single fracture because of the limited capability of the finite matrix to store solute.

On why gravel bed streams are paved

Abstract: Bedload transport in poorly sorted gravel bed streams downstream of dams is considered. Bedload and typical bed material (subpavement) size distributions are observed to be similar; it follows that the coarse half of the subpavement moves through a reach at a rate near that of the fine half. Since coarser grains are intrinsically less mobile than fine grains, it follows that some mechanism must act to nearly equalize mobility. It is hypothesized that the pavement seen in gravel bed streams at low flow is in fact in place during typical transport events capable of moving all available sizes. This pavement can provide the equalizing mechanism by exposing proportionally more coarse grains to the flow. Field data are used to quantify this concept and to develop a predictive relation for river pavement. The model indicates that pavement should be absent in most sand bed streams, in agreement with observation.

Dynamic programming applications in water resources

Abstract: The central intention of this survey is to review dynamic programming models for water resource problems and to examine computational techniques which have been used to obtain solutions to these problems. Problem areas surveyed here include aqueduct design, irrigation system control, project development, water quality maintenance, and reservoir operations analysis. Computational considerations impose severe limitation on the scale of dynamic programming problems which can be solved. Inventive numerical techniques for implementing dynamic programming have been applied to water resource problems. Discrete dynamic programming, differential dynamic programming, state incremental dynamic programming, and Howard's policy iteration method are among the techniques reviewed. Attempts have been made to delineate the successful applications, and speculative ideas are offered toward attacking problems which have not been solved satisfactorily.

The Turning Bands Method for simulation of random fields using line generation by a spectral method

Abstract: The turning bands method (TBM) for the simulation of multidimensional random fields is presented. These fields commonly occur in the Monte Carlo simulation of hydrologic processes, particularly groundwater flow and mass transport. The general TBM equations for two- and three-dimensional fields are derived with particular emphasis on the more complicated two-dimensional case. For stationary two-dimensional fields the unidimensional line process is generated by a simple spectral method, a technique which can be generally applied to any two-dimensional covariance function and which is easily extended to anisotropic and areal averaged processes. Theoretically and by example the TBM is shown to be ergodic even for a finite number of lines, and it is demonstrated that it rapidly converges to the true statistics of the field. Guidelines are presented for the selection of model parameters which will be helpful in the design of simulation experiments. The TBM is compared to other methods in terms of cost and accuracy, demonstrating that the TBM is as accurate as and much less expensive than multidimensional spectral techniques and more accurate than the most expensive approaches which use matrix inversion, such as the nearest neighbor approach. The unidimensional spectral technique presented here permits, for the first time, the inexpensive and accurate TBM simulation of any proper two-dimensional covariance function and should be of some help in the stochastic analysis of hydrologic processes.

Simulation of solute transport using a transfer function model

Abstract: A transfer function model is proposed for simulating solute transport under natural field conditions where substantial variability exists in water transport properties. This approach makes no attempt to describe the variability through a deterministic model but merely measures the distribution of solute travel times from the soil surface to a reference depth. Using this distribution function, it is possible to simulate the average solute concentrations at any depth and time for arbitrary solute inputs or water application variability. Equivalently, the model may be used to predict the probability of extremely long or short travel times for a mobile chemical. In this paper several illustrative calculations are performed for which analytic solutions are possible. In a companion paper (Jury et al., this issue) a field test of the model is reported.

Moisture and heat transport in hysteretic, inhomogeneous porous media: A matric head‐based formulation and a numerical model

Abstract: A general, physically based formulation of water and energy transport in partially saturated soil must account for the coupling between the fields of matric potential ψ and temperature T. The formulation by de Vries (1958) is converted to one that employs ψ and T as the dependent variables. This conversion facilitates a significant generalization of the theory to accommodate the omnipresent complications of hysteresis and inhomogeneity. The limitations of the assumptions of local thermodynamic equilibrium are discussed. A finite element solution algorithm for the one-dimensional equations is outlined and tested on a variety of problems. The computational results demonstrate the reliability of the numerical model.

Stochastic modeling of groundwater flow by unconditional and conditional probabilities: 2. The solute transport

Abstract: The problem of solute transport in a heterogeneous formation whose transmissivity or hydraulic conductivity are subject to uncertainty is studied for two- and three-dimensional flows. Approximate closed form solutions are derived for the case of a solute pulse in an average uniform flow through a formation of unconditional stationary random transmissivity. The solute concentration, regarded as a random variable, is determined in terms of its expectation and variance and is found to be subject to a high degree of uncertainty. The uncertainty is greatly reduced if the solute input zone is large compared to the transmissivity integral scale. In any case the concentration expectation does not obey a diffusion type equation in the case of two-dimensional flows, unless the solute body has traveled a distance larger than a few tens transmissivity integral scales. This distance may be exceedingly large in many conceivable applications.

Objective analyses and mapping techniques for rainfall fields: An objective comparison

Abstract: Many methods have been proposed and applied individually to rainfall fields in order to estimate point or average values at ungauged sites. This paper reviews some of the usual as well as some of the more recent techniques. They are classified according to their fundamental principles, optimality criteria, and practical aspects. Some theoretical developments, mostly for the statistically based techniques, are offered, and the practical aspects are mainly directed to the particular case of rainfall fields. A case study is presented for a region with particularly high rainfall variability, providing a good sample of events for testing the sensitivity of the estimation to the different methods used. The identification of statistical structure functions, required by certain methods using regionalized variable concepts, is discussed in detail for the case considered. Method evaluation is based on a classical validation technique that divides the available stations into two separate networks, i.e., a base network is used to perform estimations at the stations of a test network for a set of independent storm events. Careful attention is paid to result interpretation and visualisation. Finally, conclusions are drawn as to which method should be implemented, taking into account cost-efficiency considerations.

Ecological optimality in water-limited natural soil-vegetation systems: 1. Theory and hypothesis

Abstract: The solution space of an approximate statistical-dynamic model of the average annual water balance is explored with respect to the hydrologic parameters of both soil and vegetation. Within the accuracy of this model it is shown that water-limited natural vegetation systems are in stable equilibrium with their climatic and pedologic environments when the canopy density and species act to minimize average water demand stress. Theory shows a climatic limit to this equilibrium above which it is hypothesized that ecological pressure is toward maximization of biomass productivity. It is further hypothesized that natural soil-vegetation systems will develop gradually and synergistically, through vegetation-induced changes in soil structure, toward a set of hydraulic soil properties for which the minimum stress canopy density of a given species is maximum in a given climate. Using these hypotheses, only the soil effective porosity need be known to determine the optimum soil and vegetation parameters in a given climate.

A Model for Streamwater Chemistry at Birkenes, Norway

Abstract: A simple two-reservoir model incorporating a small number of physically realistic processes accounts for the major short-term variations in Streamwater chemistry during the snow free season at Birkenes, a 0.41-km2 gaged catchment in coniferous forest on granite bedrock in southernmost Norway. This area is in the zone of maximum deposition of acidic compounds from the atmosphere (weighted-average pH of precipitation 4.24), and the Streamwater is acidic (pH 4.48). The complete model builds on the hydrologic and sulfate submodels previously described. The cation submodel includes H+, Al, Ca, and Mg and is based on the mobile anion concept. As input data series the model requires only precipitation volume and sulfate concentration, estimates of sulfur dry deposition, and daily mean temperature. The model simulates volume and concentrations of major ions in stream-water. Chemical processes incorporated in the model include cation exchange, weathering, dissolution/precipitation of gibbsite, sulfate adsorption/desorption, and sulfate mineralization. Typical characteristics of Streamwater chemistry at Birkenes which are simulated by the model are (1) elevated sulfate concentrations in the first autumn stormflow following dry summers and the general decrease later in the autumn and (2) positive correlations between the H+ and Al concentrations and discharge and negative correlations between these factors and the Ca and Mg concentrations. The simplicity of the model and the fact that it is based on known, physically realistic processes make it particularly suitable as a tool in clarifying important mechanisms in catchments.

Passive microwave sensing of soil moisture under vegetation canopies

Abstract: Vegetation cover has a significant effect on the ability of passive microwave radiometers to detect changes in near-surface soil moisture. A quantitative technique for isolating the effect of vegetation was developed using a theoretical model as the basis of a parametric approach. This approach was evaluated using data collected by truck-mounted sensors over experimental plots. Results show that a microwave radiometer operating at a 21-cm wavelength can provide volumetric surface soil moisture estimates to ∼5% of accuracy for fields covered with moderate vegetation. In addition, all of the data required for applying the parametric model can be measured using remote sensing.

A Comparison of Four Streamflow Record Extension Techniques

Abstract: One approach to developing time series of streamflow, which may be used for simulation and optimization studies of water resources development activities, is to extend an existing gage record in time by exploiting the interstation correlation between the station of interest and some nearby (long-term) base station. Four methods of extension are described, and their properties are explored. The methods are regression (REG), regression plus noise (RPN), and two new methods, maintenance of variance extension types 1 and 2 (MOVE.l, MOVE.2). MOVE.l is equivalent to a method which is widely used in psychology, biometrics, and geomorphology and which has been called by various names, e.g., ‘line of organic correlation,’ ‘reduced major axis,’ ‘unique solution,’ and ‘equivalence line.’ The methods are examined for bias and standard error of estimate of moments and order statistics, and an empirical examination is made of the preservation of historic low-flow characteristics using 50-year-long monthly records from seven streams. The REG and RPN methods are shown to have serious deficiencies as record extension techniques. MOVE.2 is shown to be marginally better than MOVE.l, according to the various comparisons of bias and accuracy.

An upstream finite element method for solution of transient transport equation in fractured porous media

Abstract: A finite element method for the solution of two-dimensional transient dispersive-convective transport of nonconservative solute species in fractured porous media is presented. A two-nodal point one-dimensional transport element for fractures is developed which provides a number of advantages relative to conventional fracture representation by two-dimensional continuum elements. To eliminate the oscillatory behavior of convective-dominated transport which is a more likely occurrence in fracture, a very efficient one-dimensional upstreaming method along with a two-dimensional method is implemented. Validity of the numerical scheme is established by comparison with existing one- and two-dimensional analytic solutions.

Radium, thorium and radioactive lead isotopes in groundwaters: application to the in situ determination of adsorption-desorption rate constants and retardation factors

Abstract: Five groundwater samples taken from different Hydrogeologie settings in Connecticut were analyzed for major cation chemistry and the concentration of U and Th decay series nuclides 238U, 234Th, 226Ra, 222Rn, 210Pb, 210Po, 232Th, 228Ra, 228Th, and 224Ra. The concentration of 222Rn in the waters ranged between 103 and 104 dpm l−1 and was three to four orders of magnitude greater than that of the short-lived alpha daughters 224Ra, 228Ra, and 234Th, even though the rates of supply of these four nuclides to solution are expected to be similar. We infer that sorption removes radium and thorium from these groundwaters on a time scale of 3 minutes or less. The (224Ra/228Ra) and (234Th/228Th) activity ratios in these waters indicate that desorption of these nuclides occurs on a time scale of a week or less and that equilibrium between solution and surface phases is established. In situ retardation factors for radium, thorium, and lead may therefore be calculated directly from the isotopic data; values range from 4,500 to 200,000. Neither sorption time scales nor retardation factors are strongly dependent on the nuclide or on hydrogeology of the aquifer. Since our study includes nuclides with diverse chemical properties, we suggest that other uncomplexed heavy metals and transuranic elements will also behave in a manner similar to those measured here. The approach presented here should therefore find application in developing site-specific models of the transport of radioactive or stable elemental waste through water-saturated media.

Stochastic modeling of groundwater flow by unconditional and conditional probabilities: 1. Conditional simulation and the direct problem

Abstract: Mathematical modeling of groundwater flow in heterogeneous porous formations of large extent is investigated. The formation properties (hydraulic conductivity, transmissivity) as well as flow variables (head, specific discharge, solute concentration) are regarded as random variables subjected to uncertainty. The main aim of the study is to analyze the influence of conditional probability of input variables upon the statistical structure of the dependent variables. The unconditional probability density functions are supposed to be stationary multivariate normal, while conditioning accounts for the measured values at a few points of the formation. Two problems of groundwater flow are discussed in part 1: conditional simulation and the direct problem for steady flow. Analytical results are obtained by using perturbation approximations. Average uniform head gradient flows as well as recharge and flow to wells are discussed. In unconditional modeling the input variable (the conductivity or transmissivity log) is regarded as stationary and is represented by its constant mean and variogram. The ensemble of formations on which statistical calculations are carried out represents all aquifers with same probability density distributions. In conditional modeling the measured values at a few points are kept fixed and uncertainty prevails only at other points. Consequently, statistical computations are performed for the subensemble of aquifers which preserve the measured values, and as a result, both input and output variables are nonstationary. The main effect of conditioning is to reduce the variance, i.e., the uncertainty, of these variables. This effect is particularly important in the case of flow toward wells. Application of the modeling method to field problems is outlined.

Cost allocation in water resources development

Abstract: Different methods for allocating the joint costs of water supply projects among users are compared on the basis of certain commonsense principles of equity. We contrast the separable costs-remaining benefits (SCRB) method with simple proportional allocation schemes and more sophisticated methods from cooperative game theory, including the Shapley value and variants of the core. Advantages and disadvantages of the methods in practice are examined using a regional water supply system in Sweden. It is argued that these principles provide a useful framework for choosing intelligently among methods. The appropriateness of a method depends on the context, especially on the reliability of information about costs and demands. The conclusion is that there is no one best method, although from a normative standpoint the SCRB method may be one of the worst.

Tracer movement in a single fissure in granitic rock: Some experimental results and their interpretation

Abstract: Radionuclide migration was studied in a natural fissure in a granite core The fissure was oriented parallel to the axis in a cylindrical core 30 cm long and 20 cm in diameter The traced solution was injected at one end of the core and collected at the other Breakthrough curves were obtained for the nonsorbing tracers, tritiated water, and a large-molecular-weight lignosulphonate molecule and for the sorbing tracers, cesium and strontium From the breakthrough curves for the nonsorbing tracers it could be concluded that channeling occurs in the single fissure A ‘dispersion’ model based on channeling is presented The results from the sorbing tracers indicate that there is substantial diffusion into and sorption in the rock matrix Sorption on the surface of the fissure also accounts for a part of the retardation effect of the sorbing species A model which includes the mechanisms of channeling, surface sorption, matrix diffusion, and matrix sorption is presented The experimental breakthrough curves can be fitted fairly well by this model by use of independently obtained data on diffusivities and matrix sorption

A stochastic‐convective transport representation of dispersion in one‐dimensional porous media systems

Abstract: A stochastic-convective transport formulation based upon solute travel time probability is presented and is shown to include Fickian transport as a special subcase. It is further demonstrated that a travel time probability associated with a lognormal distribution of hydraulic conductivity will yield concentration breakthrough curves nearly equivalent to those of Fickian transport when the coefficient of variation in travel time is sufficiently small, i.e., less than unity. When applied to column tracer experiments, the results suggest that typical laboratory-measured hydrodynamic dispersion may be ascribed to local variations in hydraulic conductivity. Moreover, stochastic-convective transport is shown to conserve solute mass under a flux boundary condition but to fail to do so under a held concentration condition. This result indicates the importance of boundary conditions for properly formulated stochastic transport. The travel time formulation is shown to provide a direct link between measured dispersivity and the autocovariance of local flow velocity variations that are a consequence of media inhomogeneity and the system boundary conditions. Dispersivity is shown to manifest a scale effect by increasing in proportion to the length of a system when the velocity correlation range is greater than that length. An expression for the effective dispersivity is derived for the case of long-range velocity correlations and is shown to represent non-Fickian behavior.

Nonlinear equation governing flow in a saturated porous medium

Abstract: It is argued that the appropriate generalization of Darcy's law when inertia effects are included takes the form ∇p = −(μ/k) V − (ρc/k½)|V|V, div V = 0, where k is the permeability of the medium and the ‘form drag constant’ c is a coefficient which is independent of the pressure p, the seepage velocity V, and the density ρ and viscosity μ of the fluid but which is dependent on the geometry of the medium. We formulate a nonlinear extension of Brinkman's self-consistent theory for the flow of a viscous fluid through a swarm of spherical particles. We equate the drag per unit volume given by the right hand side of the first of the above equations to the total drag ND on the N particles contained within that unit volume, in an infinite region Ω, where D is the drag on a single particle placed in a velocity field v subject to ρ(v · ∇)v + grad p = μ∇2v−μ/k v − (cρ/k½)|v|v, div v = 0, v|∂Ω is a prescribed constant, where μ is the viscosity. Without solving these equations, we obtain an estimate for c from the known experimental drag law for a solid sphere placed in a uniform stream.

Effect of Viewing Angle on the Infrared Brightness Temperature of Snow

Abstract: Remote sensing of snowpack temperatures from satellites requires knowledge of the spectral emissivity of snow. A model for spectral emissivity is combined with the Planck function to calculate brightness temperature of snow in thermal infrared wavelengths for a range of grain sizes and viewing angles. Emissivity variations caused by density, grain shape, liquid water, and grain size are apparently unimportant, but emissivity varies with viewing angle to produce differences between thermodynamic temperature and brightness temperature as large as 3 K at wavelengths 12 to 14 μm, within the major atmospheric infrared window. This difference is also verified by experimental measurements. An equation to convert brightness temperatures to thermodynamic temperatures is presented, and this is also combined with a dual-wavelength atmospheric correction method. The spectral emissivity model is also used to calculate an ‘all-wave’ emissivity of snow: 0.985–0.990 for all grain sizes.

Prediction of annual floods generated by mixed processes

Abstract: In areas where the annual flood series is generated by more than one distinctive hydrologic process, the Gumbel distribution does not provide a satisfactory fit. Physical evidence is used to identify the flood-generating processes, which in the Cascade Mountains include snowmelt and rainfall. Individually, the snowmelt and rain generated annual floods are adequately modeled by simple Gumbel distributions. These distributions have to be compounded to provide a good fit to the annual floods which are produced by mixed processes.

Effects of kriging and inverse modeling on conditional simulation of the Avra Valley Aquifer in southern Arizona

Abstract: The Avra Valley aquifer in southern Arizona is modeled stochastically at three levels of uncertainty. The highest level of uncertainty occurs when log transmissivity estimates are based on measured values of this parameter but without regard to the geographic location of each measurement point. The resulting steady state hydraulic heads in the aquifer, computed by unconditional simulation with the aid of a multivariate normal random number generator coupled with a finite element model, have a relatively large variance. This variance can be reduced by conditioning the log transmissivity estimates on the spatial arrangement of the data by means of kriging. When conditional simulation of the aquifer is performed at this intermediate level of uncertainty with the aid of the same technique as in the unconditional case, the variance of the predicted head values is reduced by a factor of 3.2. The lowest level of uncertainty is achieved when the log transmissivity estimates are further conditioned on data relating to the flow regime, such as flow rates and water levels in observation wells, by means of a statistical inverse procedure. Conditional simulation at this level of uncertainty is a novel concept. It results in a hydraulic head prediction variance that is 14.3 times lower than the corresponding variance based on kriged log transmissivities. The net effect of conditioning by means of kriging and inverse modeling is to reduce the prediction variance by a factor of 46.0. A similar study performed by Binsarti (1980) on the Cortaro aquifer in southern Arizona showed insignificant variance reduction due to kriging, but a factor of four reduction after inverse modeling. These results indicate that the conditioning effect of the inverse method may be much greater than that of kriging. The fact that conditioning can reduce the hydraulic head prediction variance by as much as a factor of 46 implies that one should be cautious when dealing with the results of stochastic aquifer models in which conditioning effects are disregarded.

A geomorphoclimatic theory of the instantaneous unit hydrograph

Abstract: The instantaneous unit hydrograph is conceived as a random function of climate and geomorphology varying with the characteristics of the rainfall excess. The probability density functions of the peak and time to peak of the IUH are analytically derived as functions of the rainfall characteristics and the basin geomorphological parameters. The main characteristics of these pdf's are studied, and a new approach to hydrologic similarity is initiated under the concept of the geomorphoclimatic IUH. For a given set of geomorphologic characteristics and a particular intensity and duration of rainfall, the peak and time to peak of the IUH corresponding to those values can be easily estimated.

Effects of aggradation and degradation on riffle-pool morphology in natural gravel channels, northwestern California

Abstract: " :.:".".. ;": ~ After the flood of December 1964, 12 gaging sections in northern California widened as much as 100% and aggraded as much as 4 m, and then degraded to stable levels during a period of 5 years or more. As channels aggraded, bed material became finer, and low to moderate flow through gaging sections in pools became shallower, faster, and steeper. Comparisons of longitudinal profiles also show the diminishment of pools as well as a decrease in bar relief accompanying the excessive sediment load. As gaging sections degraded, hydraulic geometries recovered to a limited degree; full recovery probably depends on channel narrowing and further depletion of sediment supply. The hydraulic changes with aggradation indicate an increase in the effectiveness of moderate discharges (less than I- to 2-year recurrence interval, annual flood series) to transport bed load and shape the bed . Bars become smaller, pools preferentially fill, and rimes armored with relatively small gravel tend to erode headward during falling stages and form a gentler gradient. Excess sediment can thus be more readily transported out of channels when additional contributions from watersheds are usuall slight.

Beware of spurious self‐correlations!

Abstract: Spurious self-correlations arise when two parameters (sums, differences, ratios, products, or single variables) that are used in a linear regression analysis have a common term. Examples are presented to show that under certain conditions, perfect (but entirely spurious) correlation is obtained between two such parameters formed from random numbers. The magnitude of the spurious self-correlation coefficient is greatest for data sets where there is much larger dispersion in the data for the common term relative to the unique term(s) in the parameters. Logarithmic transformations or log-log plots enhance spurious self-correlations of ratios and products. The misuse of spurious self-correlation is illustrated with examples from the literature.