Showing papers in "Water Resources Research in 1979"
TL;DR: In this article, Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions, such as Tukey's lambda, which may present problems in deriving their parameters by more conventional means.
Abstract: Distributions whose inverse forms are explicitly defined, such as Tukey's lambda, may present problems in deriving their parameters by more conventional means. Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions.
1,147 citations
TL;DR: In this article, a unified synthesis of the hydrologic response of a catchment to surface runoff is attempted by linking the instantaneous unit hydrograph (IUH) with the geomorphologic parameters of a basin.
Abstract: A unifying synthesis of the hydrologic response of a catchment to surface runoff is attempted by linking the instantaneous unit hydrograph (IUH) with the geomorphologic parameters of a basin. Equations of general character are derived which express the IUH as a function of Horton's numbers RA, RB, and RL; an internal scale parameter LΩ and a mean velocity of streamflow v. The IUH is time varying in character both throughout the storm and for different storms. This variability is accounted for by the variability in the mean streamflow velocity. The underlying unity in the nature of the geomorphologic structure is thus carried over to the great variety of hydrologic responses that occur in nature. An approach is initiated to the problem of hydrologic similarity.
1,007 citations
TL;DR: In this article, regression models for estimating soil-water-retention curves from particle-size distribution, percentage of organic matter, and bulk density were presented for estimating water retention curves.
Abstract: Regression models are presented for estimating soil-water-retention curves from particle-size distribution, percentage of organic matter, and bulk density. Models were developed from the measured soil-water-retention curves of artificially packed cores (7.6×7.6 cm) of 43 soil materials. These soil materials included 13 agricultural soils. Curves predicted with these models approximated reasonably well the measured water retention of 61 Missouri soils. Because conventional methods of obtaining retention curves are expensive and time consuming, these equations will be valuable for modeling salt and water flow in soils and for estimating available water capacities.
776 citations
TL;DR: The oxygen-18 content of precipitation in the Amazon basin is characterized by a very small inland gradient, 0.75 × 10−3 ‰ km−1 as discussed by the authors, which is a consequence of the large contribution of reevaporated moisture to the basin's water balance.
Abstract: The oxygen-18 content of precipitation in the Amazon basin is characterized by a very small inland gradient, 0.75 × 10−3 ‰ km−1. This is a consequence of the large contribution of reevaporated moisture to the basin's water balance. A distinct seasonal and regional pattern of stable isotope composition has been recognized and shows the basin to be inhomogeneous from the hydrometeorological point of view. The occasional appearance of very low δ values is believed to be related to the position of the ITCZ rather than to interbasin processes.
638 citations
TL;DR: In this article, the effect of regional advection on potential evaporation and an assumed symmetry between potential and actual evaporem with respect to the evaporative power of the air was investigated.
Abstract: Actual regional evapotranspiration is calculated by means of a procedure requiring only meteorological data, which are those commonly used in the various versions of the combination approach for potential evaporation. The approach is based on a conceptual model involving, first, the effect of regional advection on potential evaporation, and second, an assumed symmetry between potential and actual evaporation with respect to the evaporative power of the air in the absence of advection. Thus the degree of nonavailability of water for evapotranspiration, that is the aridity of the region, is deduced from the regional advection of drying power of the air, as implied by the atmospheric conditions. The approach was found to give good agreement with daily data of evapotranspiration obtained by means of an energy budget method for a period of severe drought in a rural watershed in a sandy region. One of the advantages is that no soil moisture data, no stomatal resistance properties of the vegetation, nor any other additional aridity parameters are required to determine actual evapotranspiration.
527 citations
TL;DR: In this paper, a geostatistical approach is proposed for characterizing the uncertainty about the transmissivity field of an aquifer and analyzing its effect on predicted head values.
Abstract: A geostatistical approach is proposed for characterizing the uncertainty about the transmissivity field of an aquifer and analyzing its effect on predicted head values. A new methodology is developed, which couples conditional simulation and groundwater flow modeling. Conditional simulation is used for generating different two-dimensional transmissivity fields that all have the same spatial variability as the true field and are consistent with the measured T values at well locations. Two case studies are presented in order to illustrate the method, and conclusions are drawn for future investigation.
525 citations
TL;DR: In this article, a modified version of Carlson's (1977) trophic state index summarizes relationships among summer, epilimnetic measurements of total phosphorus, chlorophyll-a, and transparency.
Abstract: The feasibility of lake water quality management planning has been greatly increased over the past 10 years with the development of relatively simple, empirical methods for assessing eutrophication problems. These relate phosphorus loading, hydrology, and morphometry to such traditional trophic state indices as phosphorus concentration, chlorophyll-a concentration, and transparency. One of the difficulties associated with use of these methods is that water quality criteria, as related to beneficial use, do not generally correspond to subjective definitions of ‘trophic state.’ This paper attempts to improve upon existing methods by relating measures of phosphorus, chlorophyll-a, and/or transparency to hypolimnetic dissolved oxygen, which is of direct relevance to existing water quality standards, particularly for fisheries management. A modified version of Carlson's (1977) trophic state index summarizes relationships among summer, epilimnetic measurements of total phosphorus, chlorophyll-a, and transparency. On the basis of data from 30 lakes this index is shown to be highly correlated with areal hypolimnetic oxygen depletion rate when the apparent effects of mean depth are also taken into account (R2 = 0.91). Tests of the empirical model on a separate data base of 86 lakes indicate that the approach can be used to predict oxygen status based upon lake morphometry and trophic index. The methodology provides a link between phosphorus mass balance models and existing water quality criteria for dissolved oxygen.
519 citations
TL;DR: In this paper, a new model is presented which assumes the simple mixing of the end-members of the system (gaseous CO2 and solid carbonate) and their relative proportions are given by comparison of the molality of total dissolved carbon (measured bicarbonates and calculated H2CO3, assuming equilibrium at the temperature of the aquifer) to the mollality of dissolved carbon of inorganic origin (DIC).
Abstract: Carbon 14 age calculations are based upon the assumption that the initial activity of the material to be dated was 100% of modern CO2 activity (100 pmc). This assumption is generally good for material of organic origin (wood and, to some extent, shells). Dissolved carbon in groundwater has two main sources: active carbon from the soil zone and less active (or even ‘dead’) carbon of inorganic origin. Furthermore, the existence of a three-phase system (gaseous CO2 and aqueous and solid carbon) allows significant isotopic exchange. The estimation of the initial activity of the total dissolved carbon requires the use of a model. Existing models for the determination of the initial 14C activity (A0) of total dissolved carbon are (1) Vogel's model (A0 = 85 ± 5% of modern carbon), (2) Tamers' model (A0 is the activity of dissolved carbon of organic origin diluted by dissolved carbon of inorganic origin), (3) Pearson's model (A0 is the mixing of these same sources of carbon, evidenced by their stable isotope content), and (4) Mook's model (same as Tamers' model plus a correcting term accounting for an isotopic exchange in closed system with aqueous CO2). A new model is presented which assumes the simple mixing of the end-members of the system (gaseous CO2 and solid carbonate). Their relative proportions are given by comparison of the molality of total dissolved carbon (measured bicarbonates and calculated H2CO3, assuming equilibrium at the temperature of the aquifer) to the molality of dissolved carbon of inorganic origin (DIC). The DIC is determined on the basis of the alkaline-earth molal concentration corrected for gypsum dissolution and base exchange. This treatment can be more simply substituted for by the measurement of field alkalinity, whose value, expressed in molal concentration, is identical to twice the molal concentration of DIC. In addition to the mixing, which also leads to Tamers' expression, an isotope exchange term is calculated, assuming that a part of the contribution of either soil CO2 or solid carbonate is in isotopic equilibrium, in an open system, with the other carbon reservoir. The different models are applied to the results of the confined aquifer of the ‘calcaires carboniferes’ in northern France and Belgium. A value of −24‰ (equivalent to about −22.8‰ for gaseous CO2) is adopted for the 13C content of aqueous carbon dioxide. Values for the isotope fractionation which occurs between carbon-bearing compounds at aquifer temperatures are adopted from values of Mook et al. (1974) and Deines et al. (1974). It is assumed that ∈14C% ≃0.2∈13C‰. Radiometric ages obtained from the Vogel and Tamers approaches are undercorrected. The model of Mook appears very sensitive to the variations of δ 13C of the total dissolved carbon and can lead to overcorrected values. The model of Pearson is generally in rather good agreement with our treatment in the range of average values of A0. For extremely high and low values of A0 our model provides larger corrections. The ages obtained from the different models are also discussed on the basis of the 18O content of the waters, which appear too high to be attributed to glacial epochs. Average flow velocities calculated from our model range from 1.70 m yr−1 to 0.73 m yr−1.
471 citations
TL;DR: In this paper, the longitudinal dispersion produced as a result of vertical variations of hydraulic conductivity in a stratified aquifer is analyzed by treating the variability of conductivity and concentration as homogeneous stochastic processes.
Abstract: The longitudinal dispersion produced as a result of vertical variations of hydraulic conductivity in a stratified aquifer is analyzed by treating the variability of conductivity and concentration as homogeneous stochastic processes. The mass transport process is described using a first-order approximation which is analogous to that of G. I. Taylor for flow in tubes. The resulting stochastic differential equation describing the concentration field is solved using spectral representations. The results of the analysis demonstrate that for large time the longitudinal dispersivity approaches a constant value which is dependent on statistical properties of the medium. The analysis also describes the transient development of the dispersive process and some non-Fickian effects which occur early in the displacement process.
440 citations
TL;DR: In this paper, estimates of the parameters and quantiles of the Gumbel distribution by the methods of probability weighted moments, (conventional) moments, and maximum likelihood were compared.
Abstract: Estimates of the parameters and quantiles of the Gumbel distribution by the methods of probability weighted moments, (conventional) moments, and maximum likelihood were compared. Results were derived from Monte Carlo experiments by using both independent and serially correlated Gumbel numbers. The method of probability weighted moments was seen to compare favorably with the other two techniques.
412 citations
TL;DR: In this article, a 0.3028-ha watershed has been monitored to monitor streamflow and subsurface flow through the soil mantle at a variety of topographic locations.
Abstract: A 0.3028-ha watershed has been instrumented to monitor streamflow and subsurface flow through the soil mantle at a variety of topographic locations. The watershed is forested, with steep (35°) slopes and shallow (average 55 cm) soils on impermeable Old Man gravels. Data for a number of storms indicate that subsurface flow via ‘macropores’ (root channels, pipes) and seepage zones in the soil is the predominant mechanism of channel stormflow generation in storms with quickflows greater than about 1 mm. Subsurface flow from all parts of the watershed appears to contribute to stormflow even in very small storms (quickflow of the order of 3% of net precipitation). The saturated hydraulic conductivity of the soil matrix is not a limiting factor on the ability of subsurface flow to generate channel stormflow, because dye tracer experiments demonstrate that water may move through macropores (particularly root channels) at rates 2 orders of magnitude greater. However, subsurface flow from lower slope areas contributes to delayed flow; cessation of subsurface flow and Streamflow after a drought period is roughly coincident in time. In the study area it appears that streamflow is at almost all times dominated by subsurface flow and that runoff from partial and variable source areas contributes significant quantities of streamflow only during the rising limb of small (less than 1 mm of quickflow) flood hydrographs.
TL;DR: In this article, a stochastic analysis of two-dimensional steady state groundwater flow in a bounded domain is carried out by using Monte Carlo techniques, where the flow domain is divided into a set of square blocks and a nearest-neighbor process model is used to generate a multilateral spatial dependence between hydraulic conductivity values in the block system both statistically isotropic and statistically anisotropic autocorrelation functions are considered.
Abstract: A stochastic analysis of two-dimensional steady state groundwater flow in a bounded domain is carried out by using Monte Carlo techniques The flow domain is divided into a set of square blocks A nearest-neighbor stochastic process model is used to generate a multilateral spatial dependence between hydraulic conductivity values in the block system Both statistically isotropic and statistically anisotropic autocorrelation functions are considered This model leads to a realistic representation of the spatial variations in hydraulic conductivity in a discrete block medium Results of the simulations provide estimates of the output distributions in hydraulic head The probability distribution for hydraulic head must be interpreted in terms of the spatial variation of the expected head gradients, the standard deviation in the hydraulic conductivity distribution, the ratio of the integral scales of the autocorrelation function for conductivity to the distance between boundaries on the flow domain, and the arrangement of statistically homogeneous units within the flow domain The standard deviation in hydraulic head increases with an increase in either the standard deviation in hydraulic conductivity or the strength of the correlation between neighboring conductivity values The standard deviations in hydraulic head are approximately halved when a uniform, bounded, two-dimensional flow field is reduced to one-dimensional form The uncertainties in the predicted hydraulic head values are strongly influenced by the presence of a spatial trend in the mean hydraulic conductivity In evaluating the concept of an effective conductivity for a heterogeneous medium, both the nature of the spatial heterogeneities in hydraulic conductivity and the flow system operating within the flow domain must be considered
TL;DR: In this article, the authors used Cowan's theory for root uptake, Monteith's combination equation for vapor flux, constant internal resistance per unit of root length, and stomatal response to light, humidity, temperature, and Ψ.
Abstract: In a soil-plant-atmosphere model the soil was divided into several layers with different root densities and soil water potentials, but the aboveground portion was represented by single values both of diffusive resistance and of plant water potential Ψ. The model used Cowan's theory for root uptake, Monteith's combination equation for vapor flux, constant internal resistance per unit of root length, and stomatal response to light, humidity, temperature, and Ψ. For forests, unstressed transpiration Eu, defined as the transpiration that would occur if stomatal opening were not reduced by low Ψ, may be a more useful value than potential evapotranspiration. The model simulated field data from a hardwood forest in terms of both Ψ and stomatal behavior within a day and over a summer. Stomata had a threshold type of response to Ψ, with closure only occurring as Ψ approached a critical potential Ψc. Internal resistance was high enough that when Eu was high, Ψ became low enough to cause some stomatal closure and reduce transpiration even when soil was wet. As soil dried, potential gradient decreased because plant potential could not decline further than Ψc. But internal resistance remained generally larger than rhizosphere resistance, so decrease in uptake with soil drying depended more on the decreasing soil-plant gradient than on increasing rhizosphere resistance. Simple functions, either of total soil water content or of vertical root and soil water distribution, can be used to determine the reduction of transpiration below Eu in hydrologic models.
TL;DR: This paper describes a modification of differential dynamic programming which makes that technique applicable to certain constrained sequential decision problems such as multireservoir control problems discussed in the hydrology literature.
Abstract: This paper describes a modification of differential dynamic programming (DDP) which makes that technique applicable to certain constrained sequential decision problems such as multireservoir control problems discussed in the hydrology literature. The authors contend that the method proffered here is superior to available alternatives. This belief is supported by analysis (wherein it transpires that constrained DDP does not suffer the ‘curse of dimensionality’ and requires no discretization) and computational experimentation (wherein DDP is found to quickly locate solutions of 4-reservoir problems introduced by other investigations as well as the solution of a 10-reservoir problem thought to be beyond the capability of alternative methods).
TL;DR: In this paper, a new statistically based approach to the problem of estimating spatially varying aquifer transmissivities on the basis of steady state water level data is presented, which involves solving a family of generalized nonlinear regression problems and then selecting one particular solution from this family by means of a comparative analysis of residuals.
Abstract: A new statistically based approach to the problem of estimating spatially varying aquifer transmissivities on the basis of steady state water level data is presented. The method involves solving a family of generalized nonlinear regression problems and then selecting one particular solution from this family by means of a comparative analysis of residuals. A linearized error analysis of the solution is included. This analysis allows one to estimate the covariance of the transmissivity estimates as well as the square error of the estimates of hydraulic head. In addition to the explicitly statistical orientation of the method, it has an additional feature of permitting the user to incorporate a priori information about the transmissivities. This information may be based on actual field data such as pumping tests, or on statistical data accumulated from similar aquifers elsewhere in the world. A highly efficient explicit numerical scheme for solving the inverse problem in an approximate manner when errors in water level data are sufficiently small is also described. When these errors are large, the explicit scheme may still be useful for obtaining a rapid initial idea about the approximate location of the optimum solution. Paper 1 presents the theory and illustrates it by a theoretical example. The purpose of this example is to demonstrate the effectiveness of our method in dealing with noisy data obtained from a known model. Application of the method to real data will be described in paper 2.
TL;DR: In this paper, a classification of aquifers is proposed based on the frequency distribution of the permeability frequency distribution and its autocorrelation, which is based on three basic length scales (l, microscale; £, integral scale of K autocore correlation; and L, length scale of space change of average K).
Abstract: Most natural porous formations display significant variations in space of permeability K and storativity S. Such formations are regarded as random structures characterized by the permeability frequency distribution and its autocorrelation. With the aid of three basic length scales (l, microscale; £, integral scale of K autocorrelation; and L, length scale of space change of average K) a classification of aquifers is suggested. A similar classification is proposed for the flow regimes. The study is limited to statistically homogeneous or slowly varying formations (£ ≪ L) and to uniform or slowly varying (in space and time) flows. In the section dealing with steady flows, effective permeability, as well as variances of head gradient, specific discharge, and head, is computed for one-, two-, and three-dimensional flows. Bounds and an estimate of the effective permeability in terms of a log normal permeability distribution are given. The computations are based on physical, simplified models of formation structure. It is shown that the head variance is grossly overestimated for one-dimensional flow through blocks ‘in series,’ and the same is true for specific discharge for layers ‘in parallel.’ The two- and three-dimensional variances are much lower and are close to each other. The unsteady flow is analyzed with the aid of the relaxation time needed for blocks of different K, S to adapt to the environment. For flows which change slowly and uniformly the effective permeability is that derived for steady uniform flows, and the effective storativity is equal to the S arithmetic mean. The head gradient variance computed with the aid of some physical models is compared with that of steady uniform flow, and it is shown that for sufficiently slow time changes the flow field can be considered momentarily uniform. The various results are employed to estimate effective properties, as well as fluctuations of the head and specific discharge, in aquifers, with possible applications to prediction, the inverse problem, and hydrodynamic dispersion.
TL;DR: In this article, Monte Carlo simulation is used to study the effects of random distribution of soil properties on distribution of ponding time, composite areal rate, and bias due to variability in space.
Abstract: Monte Carlo simulation is employed to analyze the effects of random distribution of soil infiltration properties on the hydrologic performance of catchment areas. Soil hydraulic parameters are distributed with log normal distribution as reported from previous field measurements. Although independent sampling units are assumed, a discussion is presented on the nature and effect of spatial dependence. The composite infiltration rate of an area is simply the average, at an instant in time, of the infiltration rate of all points within that area. Rigorous treatment of the topic is a forbidding problem in stochastic differential equations. Monte Carlo simulation is used here to study the effects of random distribution of soil properties on distribution of ponding time, composite areal rate, and bias due to variability in space. More accurate treatment for watershed studies must also consider interaction of various points on the surface by way of overland flow paths. A distributed watershed simulation model is used for this purpose to demonstrate hydrograph bias due to deterministic spatial variability, and from random variation, plus the relation of bias to rainfall rate. An analysis is also made of the partial area contribution in early parts of storm runoff caused solely by random variation in surface soil properties.
TL;DR: In this paper, an analysis that explicitly relates the amount of time that runoff water has been in contact with watershed soils to the resulting dissolved-solids concentration shows that simple mass balance chemistry methods for hydrograph separation are misleading.
Abstract: The difference between the dissolved-solids concentration in base flow and in storm flow has often been used as the basis for separating components of flow. However, an analysis that explicitly relates the amount of time that runoff water has been in contact with watershed soils to the resulting dissolved-solids concentration shows that simple mass balance chemistry methods for hydrograph separation are misleading. Field studies of surface and subsurface storm flow, when coupled with laboratory determination of the relationship between contact time and dissolved solids content of a soil water mixture, suggest that the residence time of infiltrated water is as short as a few hours in the cases studied. In those cases, hydrograph separation methods based on the simple mass balance equation for the dissolved solids will yield considerable overestimates of the base flow component.
TL;DR: In this paper, an assessment of the importance of precipitation accuracy on the rainfall-runoff modeling of a small catchment was performed using two mathematical models: a deterministic rainfall runoff model based on the kinematic wave approximation and a nonstationary time-varying multidimensional rainfall generation model.
Abstract: This study is an assessment of the importance of precipitation accuracy on the rainfall-runoff modeling of a small catchment Two mathematical models were used in the investigation: a deterministic rainfall-runoff model based on the kinematic wave approximation and a nonstationary time-varying multidimensional rainfall generation model It is implicitly assumed that this rainfall generation model is an appropriate mathematical representation of the natural phenomenon of rainfall The deterministic rainfall-runoff model is used to represent the 265-mi2 catchment of the Rio Fajardo in northeastern Puerto Rico The rainfall model generates synthetic rainfall which serves as the input to this runoff model The influence of the spatial distribution of the rainfall input on the discharge is analyzed by using 1 rain gage or 20 rain gages to record the synthetic storms The isohyetal maps and hyetographs of the synthetic storms, together with the storm hydrographs produced by the runoff model, are analyzed, with specific attention given to the volume of storm runoff, time-to-peak runoff, and peak runoff The experiments show that the spatial distribution of rain and the accuracy of the precipitation input have a marked influence on the outflow hydrograph from a small catchment
TL;DR: In this paper, the authors examined the validity of the Poisson distribution in probability models of the partial duration series and showed that when all the data are considered jointly, the assumption has to be rejected, although it is acceptable in some cases.
Abstract: The Poisson process is frequently encountered in probability models of the partial duration series. This paper looks at the necessity for specifying the model in detail by such a process and also examines the validity of the Poisson distribution, in this context, as judged on data from 26 gaging stations on 20 catchments in Great Britain. When all the data are considered jointly the Poisson assumption has to be rejected although it is acceptable in some cases. It is also suggested that if dependence exists in the partial duration series it should be looked for in the point process from which the series arises rather than among successive peak magnitudes.
TL;DR: In this paper, an equation that predicts downcoming long-wave radiation from clear skies on the basis of screen air temperature and vapor pressure has been developed, which fits measured data at extremes of temperature and humidity better than existing equations, and exhibits comparable accuracy at intermediate values.
Abstract: An equation that predicts downcoming long-wave radiation from clear skies on the basis of screen air temperature and vapor pressure has been developed. It fits measured data at extremes of temperature and humidity better than existing equations, and exhibits comparable accuracy at intermediate values.
TL;DR: In this paper, the physics of water transfer in the complete domain defined by both the saturated and unsaturated zones of soil is studied in relation to the recharge of a water table aquifer.
Abstract: Transient two-dimensional water flow is studied in relation to the recharge of a water table aquifer. The approach is based on the physics of water transfer in the complete domain defined by both the saturated and unsaturated zones of soil. Experimental data were first obtained in a slab of soil (3 m in length, 2 m in height, and 5 cm in thickness) in which the changes of water content and water pressure occurring in the flow domain were measured throughout an artificial recharge event. These were compared with the predictions of a numerical model based on the continuity of transfer between the unsaturated and saturated zones. The validity of the model is proved by the excellent agreement between simulated and experimental results. Furthermore, comparison with the results obtained by a viscous flow analog reveals the errors associated with the traditional free surface approach, which neglects transfer in the unsaturated zone.
TL;DR: In this article, two alternative mathematical models are presented that are suitable for numerical simulation of geothermal reservoirs, which are composed of two nonlinear partial differential equations, posed in terms of fluid pressure and enthalpy, and appropriate boundary conditions.
Abstract: Two alternative mathematical models are presented that are suitable for numerical simulation of geothermal reservoirs. The general mathematical model describes the three-dimensional flow of single-component water (both one and two phase) and the transport of heat in porous media. It is composed of two nonlinear partial differential equations, posed in terms of fluid pressure and enthalpy, and appropriate boundary conditions. An alternative quasi-three-dimensional model is derived by partial integration (in the vertical dimension) of the three-dimensional equations. The reservoir is assumed to have good vertical communication so that vertical equilibrium (gravity segregation) between steam and water is achieved. The resulting equations, posed in terms of vertically averaged pressure and enthalpy, include effects of an inclined, variable-thickness reservoir and mass and energy leakage to confining beds.
TL;DR: In this paper, a thin lens of rapidly moving fresh groundwater overlies a regional thick body of nearly stagnant saline groundwater that is close to ocean water in chemical composition, and two chemically distinct groundwaters are separated by a thin zone of dispersion, and both are at or slightly beyond saturation with respect to calcite.
Abstract: Xel Ha is a lagoon whose location and morphology are partly controlled by the fracture pattern in upper Pleistocene coral reef limestone. Chemical, isotopic, and hydrologic observations were made nearby where groundwater could be sampled. In addition, similar observations along vertical profiles were made at stations within the lagoon. A thin lens of rapidly moving fresh groundwater overlies a regional thick body of nearly stagnant saline groundwater that is close to ocean water in chemical composition. These two chemically distinct groundwaters are separated by a thin zone of dispersion, and both are at or slightly beyond saturation with respect to calcite. Where these two end-member groundwaters mix to form the brackish dispersion zone, the resulting solution is undersaturated with respect to calcite. This was confirmed by mass transfer and isotopic modeling which show that the mixing of two solutions of different ionic strength, each saturated with respect to calcite, can result in an undersaturated solution. Model calculations indicate that as much as 1.23 mmol of CaCO3 may be dissolved per kilogram of water. We hypothesize that many of the cuspate beaches along the east coast of the Yucatan formed in this manner and that mixing of waters of different chemistry may be an important geomorphic process in similar geologic-hydrologic settings.
TL;DR: The Late Cretaceous Fox Hills Formation and the basal portion of the overlying Hell Creek Formation constitute an important aquifer in the Fort Union coal region as discussed by the authors, which is at depths ranging from 1000 to 2000 ft, except for exposures along the Cedar Creek anticline.
Abstract: The Late Cretaceous Fox Hills Formation and the basal portion of the overlying Hell Creek Formation constitute an important aquifer in the Fort Union coal region. Throughout most of southwestern North Dakota and northwestern South Dakota the aquifer is at depths ranging from 1000 to 2000 ft, except for exposures along the Cedar Creek anticline. Water flows in the aquifer from southwest to northeast, with flow rates of a few feet per year. The recharge and discharge areas of the aquifer are separated by a north-south trending transition zone in which significant changes in water chemistry occur. Dissolved constituents in the recharge area (the western part of the study area) are Na+ = 18 mmol/l, Cl− = 0.7 mmol/1, SO42− = 2.7 mmol/1, and HCO3− = 13 mmol/l (δ13C = −12‰) with pH = 8.5. Ca2+, Mg2+, and K+ are each less than 0.1 mmol/l, dissolved O2 = 0, and traces of H2S and CH4 are present. Computer modeling and carbon isotope data suggest the following reactions in the recharge area. CO2 derived from lignitic carbon reacts to dissolve carbonate minerals, with cations then being exchanged for Na+ on clay minerals. The high pH in the aquifer is the result of buffering by carbonate-ion exchange equilibria. In the discharge area, pH values have declined to 8.3, Cl− has increased from 0.7 to 5.5 mmol/l, with a parallel increase in Na+ SO42− has essentially disappeared, HCO3− has increased from 13 to 21 mmol/l (δ13C = −9‰), CH4 has attained concentrations greater than 0.5 mmol/l, and small amounts of He are present. Traces of H2S are present, and Ca2+, Mg2+, and K+ concentrations remain low throughout the aquifer: These changes can be accounted for by reactions in the aquifer: (1) sulfate reduction to pyrite with lignitic material as the carbon source and (2) continuous buffering of pH by the carbonate-ion exchange equilibria. Chemical and hydrologic data suggest that the increase in NaCl results from upward movement of small volumes of water into the Fox Hills aquifer from the transition zone eastward. Redox reactions in the aquifer are closely analogous to those observed in pore waters of reducing marine sediments. Reactions approach but do not achieve true thermodynamic equilibrium. Measurements of redox potential suggest a downgradient decrease in redox potential. The measurements are not amenable to quantitative interpretation.
TL;DR: In this article, the authors investigated the theoretical and practical aspects of modeling water and heat flow in an unsaturated-saturated flow domain and developed a general and versatile computer simulation program for modeling coupled non-isothermal transport.
Abstract: This work investigates the theoretical and practical aspects of modeling water and heat flow in an unsaturated-saturated flow domain. Field experiments were designed and complementary laboratory analyses were employed to measure the relevant physical quantities that would enable the significance of non-isothermal effects to be determined. The Philip and de Vries non-isothermal flow model was adapted to the more general pressure (or matric) head-based approach and a new expression for the thermal liquid water diffusivity DTl is proposed. A general and versatile computer simulation program for modeling coupled non-isothermal transport is developed. The influence of coupling on diurnal subsurface moisture and heat transfer is evaluated by comparing the isothermal and non-isothermal transient numerical solutions to the heat and water transport problem. The results confirmed that coupling does not noticeably influence the temperature field, but does affect the evaporation and subsurface moisture fluxes. The non-isothermal theory is applied to calculate evaporation from dry land surfaces.
TL;DR: In this article, a technique for generating an approximate or an exact representation of the non-inferior set for problems with two objectives is presented, where the approach proceeds by using the slope of the line segment between adjacent, previously generated nonsmooth extreme points to find new non-insider solutions to improve the approximation or to establish the noniniority of the segment when the entire line segment is to be generated.
Abstract: A technique for generating an approximate or an exact representation of the noninferior set for problems with two objectives is presented. The approach proceeds by using the slope of the line segment between adjacent, previously generated noninferior extreme points to find new noninferior solutions to improve the approximation or to establish the noninferiority of the line segment when the entire noninferior set is to be generated. The proposed technique compares favorably with other generating techniques when the analytical goal is to approximate the noninferior set. A major innovation is the computation of the maximum possible error, which the analyst may control, to obtain an approximation of a desired degree of accuracy. A small example and a river basin planning problem of moderate size are used to demonstrate the use of the algorithm. Further research is required to extend the algorithm to problems with more than two objectives.
TL;DR: In this paper, nine different methods of weighting interblock hydraulic conductivity values used for modeling one-dimensional water transfer in homogeneous unsaturated soil are tested for their influence upon the accuracy of the finite difference solution.
Abstract: Nine different methods of weighting interblock hydraulic conductivity values used for modeling one-dimensional water transfer in homogeneous unsaturated soil are tested for their influence upon the accuracy of the finite difference solution. On the basis of these results the most suitable weighting relation is selected. In a first stage the numerical results obtained by the models using the various conductivity weighting formulas are compared with the quasi-analytical solution developed by Philip for a clay soil. In a second stage the models are used to simulate a laboratory experiment carried out on a sandy soil. In both cases, rather drastic boundary conditions are applied. It appears clearly from these tests that the weighting errors are of critical influence on the accuracy of solution. As proposed in this note, the geometric mean taken over two adjacent hydraulic conductivity values is the only weighting method that generates little weighting error. The latter weighting relation is found to be preferable in terms of flexibility, precision, and feasibility.
TL;DR: In this article, residential water demand is estimated as a function of temperature, rainfall, house value, water price, and household size using monthly cross-section and time-series meter readings from 261 residential households in Raleigh, North Carolina, between May 1969 and December 1974.
Abstract: Residential water demand is estimated as a function of temperature, rainfall, house value, water price, and household size using monthly cross-section and time-series meter readings from 261 residential households in Raleigh, North Carolina, between May 1969 and December 1974. Tests for validity of assumptions are made, and a methodological approach is used that provides unbiased estimates of parameters and standard errors with data that exhibit serially correlated residuals. Demand relations are estimated for total residential, winter, and sprinkling demands. Sprinkling use per period per customer for each year is estimated by subtracting winter (November–April) from summer (May–October) use. Household size explained the largest proportion of the variation in the data. Estimated sprinkling demand was found to be highly responsive to changes in water price and the level of the climatic variables, while total residential demand and winter demand were less responsive to price changes.
TL;DR: In this paper, the effects of soil spatial variability on the water balance components of a grassland watershed near Chickasha, Oklahoma, were studied by using a simulation model based on the measured properties of α (log normally distributed with an arithmetic mean of 1.0 and coefficient of variation of 0.6).
Abstract: Scaling theory, based on the similar media concept, provides a basis for representing soil spatial variability in terms of a single stochastic variable, the scaling factor α, which is related to the microscopic characteristic length of the soil. Based on the measured properties of α (log normally distributed with an arithmetic mean of 1.0 and coefficient of variation of 0.6), the effects of soil spatial variability on the water balance components of a grassland watershed near Chickasha, Oklahoma, were studied by using a simulation model. Monthly simulations of evapotranspiration, surface runoff, deep drainage, and change in soil water storage for the year 1973 were computed for several values of α representing soils with widely ranging hydraulic properties. At any time, vegetation and meteorological parameters were the same for all the soils. Our studies reveal the complexities of soil-plant-atmospheric interactions in evaluating the influence of soil variability on water balance and underline the limitations of drawing generalizations. The conclusions are highly dependent on the extent of variability (coefficient of variation of α), the frequency distribution function of the scaling factor, and the soil-plant-weather combination.