摘要:

The process formed by a sequence of cumulative departures from the mean or from some other constant (residual mass curve, cusum chart) is a popular tool for the representation and analysis of time series in many sciences, for example, in hydrology, climatology, economics, game theory. In these and other natural and social sciences, similar cumulative processes also often arise naturally; examples include fluctuations of storage in a dam with a constant release rate, lake levels, volume of glaciers, biomass, inventories, and bank accounts. Moreover, many natural economic and other phenomena may represent, or contain, components of cumulative processes of higher orders, i.e., cumulative processes of cumulative processes. In this paper we show that for a sample {yt(0)}≡{xt} of any finite sizeN, the pure cumulative process ofnth order,yt(n)≡∑i=1t(yi(n−1)− μ(n−1)), where μ(n−1)is the sample mean of {yt(n−1)} andt=1, 2, …,N, converges forn→∞ to a sine wave with a period equal to an integral fraction of the sample sizeN. This happens for any initial sample {yt(0)} and the convergence is of an exponential order. For samples from most stochastic as well as deterministic processes, the period of the limiting sine wave is equal to the sample sizeN. This behavior is demonstrated by examples involving samples from various processes ranging from pure random series to various deterministic series and including time series of some natural processes such as streamflow, lake levels, and glacier volumes. The paper includes a demonstration of effects of noise superimposed on, and of error in the value of, sample mean on the rate of convergence, and a discussion of some practical implications of the phenomenon described; it brings together some aspects of the work of Slutzky (1937), Hurst

ISSN:0043-1397    

DOI:10.1029/WR024i001p00093

年代:1988

数据来源: WILEY

摘要:

The Fort River watershed in central Massachusetts receives precipitation with a composition similar to that in Hubbard Brook (New Hampshire), yet the average stream water chemistry is substantially different, showing higherpH and TDS. This is largely a function of bedrock and surficial geology, and chemical differences among small streams within the Fort River watershed are apparently controlled by the composition and thickness of the prevailing surficial cover. The surficial deposits determine groundwater and surface water flow paths, thereby affecting the resultant contact time with mineral matter and the chemistry of the runoff. Despite the rural setting, over 95% of the annual sodium and chloride in the streams comes from road salt; after correcting for this factor, cation denudation rates are about equal to those at Hubbard Brook. However, silica removal is occurring at a rate more than 30% greater in the Fort River. When climatic conditions in Hubbard Brook and Fort River are normalized, weathering rates appear consistently higher in the Fort River, reflecting differences in weathering processes (i.e., cation exchange and silicate breakdown) and hydrogeology. Because of uncertainties in mechanisms of cation removal from watersheds, the silica denudation rate may be a better index of weathering intensity.

ISSN:0043-1397    

DOI:10.1029/WR024i001p00105

年代:1988

数据来源: WILEY

摘要:

In the present paper, attempts are made to develop solutions to various models of slug tests that may be applicable in analyzing the results of such tests where existing solutions are inadequate. Various geometries that may be encountered in heterogeneous systems such as fractured rocks are considered. Solutions are presented for linear flow, radial flow with boundaries, two layer, and concentric composite models with different flow geometries between the inner and outer region. Solutions are obtained in Laplace space and inverted back to real space numerically. Type curves are presented for each solution. Analyses of the type curves and derivative response curves reveal that many curves have unique shapes only for certain combination of the flow parameters and the distance. Other sets of type curves are similar in shape, although log‐log plots and derivative plots may emphasize some features that may not be apparent in semilog plots. These results show that slug tests suffer problems of nonuniqueness to a greater extent than other well test

ISSN:0043-1397    

DOI:10.1029/WR024i001p00115

年代:1988

数据来源: WILEY

摘要:

Dissolved oxygen (DO) is ubiquitous in Tucson basin groundwater; however, its distribution is systematic and distinct facies are apparent. Dissolved oxygen concentrations approach a minimum of 15% of the saturation limit in a chemically immature recharge facies and then rapidly increase downgradient. Groundwater throughout most of the central basin remains nearly saturated with dissolved oxygen for thousands of years during the course of its chemical evolution. DO concentrations were lowest where the water table was highest, indicative of the oxidation of phreatophyte detritus. Transverse dispersive influx of dissolved oxygen from the vadose atmosphere into the shallow phreatic zone represents an inferred process controlling the electrochemical evolution of groundwater within this aquifer. Traditional models which describe a progressive reduction of the electrochemical state of groundwater along the flow path cannot be directly applied to the Tucson basin which is a “dispersive influx‐dominated” s

ISSN:0043-1397    

DOI:10.1029/WR024i001p00127

年代:1988

数据来源: WILEY

摘要:

The techniques of locations systems analysis are adapted to develop a siting model for wastewater treatment facilities when the wastewater sources and treatment facilities are in a chain or linear configuration. The regional facility problem is considered as a special variant of the fixed charge plant location model rather than the general transshipment type model. The definition of the additional cost of a waste source joining a regional facility and the development of sequential priority constraints in the siting model allow the siting model to be conveniently solved by widely available linear programming packages. The model deals with the situation in which no current treatment is provided, no bypassed plants are allowed, a fixed level of treatment is required, and water quality constraints are either not included or are not binding. The concave cost of treatment at a plant is approximated by a fixed charge and one straight‐line segment. Numerical examples are included to demonstrate the computational efficiency of the siting mode

ISSN:0043-1397    

DOI:10.1029/WR024i001p00137

年代:1988

数据来源: WILEY

摘要:

Analytic solutions are presented for a nonlinear diffusion‐convection model describing constant rate rainfall infiltration in uniform soils and other porous materials. The model is based on the Darcy‐Buckingham approach to unsaturated water flow and assumes simple functional forms for the soil water diffusivityD(θ) and hydraulic conductivityK(θ) which depend on a single free parameterCand readily measured soil hydraulic properties. TheseD(θ) andK(θ) yield physically reasonable analytic moisture characteristics. The relation between this model and other models which give analytic solutions is explored. AsC→ ∞, the model reduces to the weakly nonlinear Burgers' equation, which has been applied in certain field situations. At the other end of the range asC→1, the model approaches a Green‐Ampt‐like model. A wide range of realistic soil hydraulic properties is encompassed by varying theCparameter. The general features of the analytic solutions are illustrated for selectedCvalues. Gradual and steep wetting profiles develop during rainfall, aspects seen in the laboratory and field. In addition, the time‐dependent surface water content and surface water pressure potential are presented explicitly. A simple traveling wave approximation is given which agrees closely with the exact solution at comparatively early

ISSN:0043-1397    

DOI:10.1029/WR024i001p00145

年代:1988

数据来源: WILEY

摘要:

In paper 1 (Broadbridge and White, this issue) an analytical nonlinear model for constant rate rainfall infiltration was proposed which promised considerable versatility. In it a wide range of soil hydraulic properties are generated through the variation of a single free parameterC. Here three techniques are advanced for determining this parameter. The first, a one‐dimensional technique, involves simultaneous determination of sorptivity and wetting front position. The second uses measured values of surface water content at long infiltration times for rainfall rates less than the saturated conductivity. In the third, three‐ and one‐dimensional flow rates are measured on the same soil sample. All are suitable for field applications. The practical range of theCparameter, for a variety of repacked and in situ soils, is found to be restricted to between 1 and 2. The hydraulic conductivities and diffusivities of the model are in general agreement with independent measurements. Its moisture characteristics ψ(θ), which are not matched in any way to measured characteristics, follow closely those observed. Also, the model permits predictions of the dependence of sorptivity on antecedent water content given a single measurement of sorptivity. The analytic solutions for constant flux infiltration given in paper 1 (Broadbridge and White, this issue) describe satisfactorily the evolution of water content profiles and surface water pressure potential in the laboratory and field without a posteriori adjustments. The mathematically simple, traveling wave approximation agrees well with observations at comparatively short infiltration times. Finally, field and laboratory measured times to ponding are predicted satisfactorily by the model's analytic exp

ISSN:0043-1397    

DOI:10.1029/WR024i001p00155

年代:1988

数据来源: WILEY

摘要:

A 231‐year reconstruction of annual precipitation, from 1750 through 1980 A.D., was developed from 10 tree ring chronologies (9 post oak,Quercus stellata, and 1 white oak,Q. alba, series) in the south‐central United States. Straight line regression was used to calibrate regionally averaged precipitation with ring width data, and the derived reconstruction was verified with independent climatic data and historical evidence. A variance trend in the tree ring data, which may have resulted from nonclimatic factors, was removed. The reconstructed precipitation series indicates that (1) a drought which appears to have been more severe than any in the instrumental record occurred about 1860 and (2) severe and prolonged droughts comparable to twentieth century events have occurred at roughly 15‐ to 25‐year intervals throughout the past 231 years. It follows that serious droughts in the south‐central United States could be expected to recur even in the absence of projected CO2‐indu

ISSN:0043-1397    

DOI:10.1029/WR024i001p00163

年代:1988

数据来源: WILEY

摘要:

The sampling efficiencies of two slightly different Helley‐Smith‐type bed load samplers were compared under carefully controlled field conditions. The samplers were identical in all respects except for the thickness of the metal used in their construction. The test results indicate that for coarse‐grained sand bed load, the sampler with a wall thickness of 1.5 mm has a sediment trap efficiency that can be as much as two times that of the sampler with walls that are 6.3 mm thick. In a separate test, bed load transport was monitored at a single channel cross section during a 10‐hour period of steady discharge. At individual sampling stations, measurement values ranged from nearly 0 to 3 times the mean. Composite bed load transport rates for full traverses of the channel width varied by a fact

ISSN:0043-1397    

DOI:10.1029/WR024i001p00173

年代:1988

数据来源: WILEY

摘要:

A computer‐based numerical analysis of the equation describing water movement in unsaturated porous materials is used to provide data on the shape of the water content profile and the thickness of the draining capillary fringe during extended gravity drainage when the water table is permitted to fall at a constant velocity to a considerable depth below the surface. These velocities of water table fall are considered in conjunction with zero and nonzero surface flux conditions. The numerical results are used to assess the validity of an approach based on the assumption that during extended drainage the draining profile retains its shape with continued water table movement. For the zero flux case the assumption is of limited use whereas, in the presence of an applied surface flux, the profile shape may be accurately defined depending on the magnitude of the rate of water table fall. In calculations involving the thickness of the draining capillary fringe the equations developed using the constant shape assumption reduce to the equivalent Green and Ampt form

ISSN:0043-1397    

DOI:10.1029/WR024i001p00178

年代:1988

数据来源: WILEY