摘要:

The objective of this paper is to review the state‐of‐the‐art of mathematical models developed for reservoir operations, including simulation. Algorithms and methods surveyed include linear programming (LP), dynamic programming (DP), nonliner programming (NLP), and simulation. A general overview is first presented. The historical development of each key model is critically reviewed. Conclusions and recommendations for future research are pres

ISSN:0043-1397    

DOI:10.1029/WR021i012p01797

年代:1985

数据来源: WILEY

摘要:

The adaptation of input‐output models for normative (benefit‐cost) appraisal of state or regional water plans is discussed. The economic surplus approach is taken to be appropriate for regional, as well as for national program appraisals. A conceptual framework, based on a willingness to pay concept, is developed to provide a formula for estimating direct economic benefits of state water development plans from input‐output models. Key elements of the formula are the costs (including opportunity costs) of primary resources utilized by water users particularly capital, labor, management, and land. A number of influential empirical studies are shown to incorrectly account for opportunity costs facing water users in producing sectors, thereby reporting erroneously high measures of economic ben

ISSN:0043-1397    

DOI:10.1029/WR021i012p01819

年代:1985

数据来源: WILEY

摘要:

An optimal control algorithm based on the discrete maximum principle is applied to multireservoir network control. Variable metric techniques are used for direct solution of the resulting two‐point boundary value problem. State variable constraints are considered by use of penalty functions. Computer time and storage requirements are moderate and increase roughly linearly with the problem dimension. Application to a 10‐reservoir network demonstrates efficacy of the proposed algori

ISSN:0043-1397    

DOI:10.1029/WR021i012p01824

年代:1985

数据来源: WILEY

摘要:

Optimization models do not perfectly represent the real world. Therefore the mathematically optimal solution is not necessarily the “best” decision to implement. Water resources planning models tend to have many solutions that are nearly optimal in terms of objective function value, but which are significantly different decisions. Methods for generating nearly optimal solutions to linear programming models have been devised. The use of such methods is illustrated with an example problem involving the sizing of reservoirs and hydroelectric power plants and demands for municipal water supply and irrigation. The results show that the interactions among the decision variables and the economics of the system determine the range of choice among nearly optimal decisions. The examination of these interactions yields insight into the basic structure of the decision prob

ISSN:0043-1397    

DOI:10.1029/WR021i012p01831

年代:1985

数据来源: WILEY

摘要:

The topography‐based, variable contributing area model of catchment hydrology of K. J. Beven and E. F. Wood (1983) was adapted for continuous simulation and extended to take account of observed processes in White Oak Run, a small forested catchment in Shenandoah National Park, Virginia. Automatic calibration of the model was attempted using eight different objective functions. All objective functions were indifferent to many of the model parameters and thus parameter estimation could not be done reliably. On the basis of results from a regionalized sensitivity analysis, the original model structure was greatly simplified. The parameters of the simplified model, which produced fits to the measured data very nearly as good as did the more complex model, were estimated well using a sum of squared errors criterio

ISSN:0043-1397    

DOI:10.1029/WR021i012p01841

年代:1985

数据来源: WILEY

摘要:

Finite difference and finite element methods are frequently used to study aquifer flow; however, additional analysis is required when model parameters, and hence predicted heads are uncertain. Computational algorithms are presented for steady and transient models in which aquifer storage coefficients, transmissivities, distributed inputs, and boundary values may all be simultaneously uncertain. Innovative aspects of these algorithms include a new form of generalized boundary condition; a concise discrete derivation of the adjoint problem for transient models with variable time steps; an efficient technique for calculating the approximate second derivative during line searches in weighted least squares estimation; and a new efficient first‐order second‐moment algorithm for calculating the covariance of predicted heads due to a large number of uncertain parameter values. The techniques are presented in matrix form, and their efficiency depends on the structure of sparse matrices which occur repeatedly throughout the calculations. Details of matrix structures are provided for a two‐dimensional linear triangular finite element

ISSN:0043-1397    

DOI:10.1029/WR021i012p01851

年代:1985

数据来源: WILEY

摘要:

In contrast to the saturated zone within which fluid moves rapidly along fractures, the fractures (with apertures large relative to the size of matrix pores) will desaturate first during the drainage process, and the bulk of fluid flow would be through interconnected pores in the matrix. Within a partially drained fracture, the presence of a relatively continuous air phase will produce practically an infinite resistance to liquid flow in the direction parallel to the fracture. The residual liquid will be held by capillary force, in regions around fracture contact areas where the apertures are small. Normal to the fracture surfaces, the drained portion of the fractures will reduce the effective area for liquid flow from one matrix block to another matrix block. A general statistical theory is constructed for flow along the fracture and for flow between the matrix blocks to the fractures under partially saturated conditions. Results are obtained from an aperture distribution model for fracture saturation, hydraulic conductivity, and effective matrix‐fracture flow areas as functions of pressure. The effects of distortion of flow paths by the air pockets are taken into account by a phase‐separation constriction factor in a generalized cubic law for fracture flow under a partially saturated condition. The reduction of matrix‐fracture flow area is taken into account by summing the aperture distribution function to a saturation cutoff aperture, which is inversely proportional to the suction head. Drainage from a column of fractured tuff is simulated using available parameters for the densely welded tuff of the Topopah Spring Member at Yucca Mountain, southern Nevada. The column is bounded by discrete vertical fractures and dissected by horizontal fractures with the fracture spacings determined by the frequencies and orientations of fractured cores. The fraction of fracture surfaces with coatings is assumed to correspond to the fraction of in situ fracture contact area. The characteristic curves for the matrix are based on laboratory measurements of tuff samples. From the cases simulated for the fractured, porous columns with discrete vertical and horizontal fractures and porous matrix blocks explicitly taken into account, it is observed that the highly transient changes from fully saturated conditions to partially saturated conditions are extremely sensitive to the fracture properties. However, the quasi‐steady changes of the fluid flow of a partially saturated, fractured, porous system could be approximately simulated without taking the fractures into

ISSN:0043-1397    

DOI:10.1029/WR021i012p01861

年代:1985

数据来源: WILEY

摘要:

An exact analog exists between steady quasi‐linear flow in unsaturated soils and porous media and the scattering of plane pulses, and the analog carries over to the scattering of plane harmonic waves. Numerous established results, and powerful techniques such as the Watson transform, are thus available for the solution and understanding of problems of unsaturated flow. These are needed, in particular, to provide the asymptotics of the physically interesting and practically important limit of flows strongly dominated by gravity, with capillary effects weak but nonzero. This is the limit of larges, withsa characteristic length of the water supply surface normalized with respect to the sorptive length of the soil. These problems are singular in the sense that ignoring capillarity gives a totally incorrect picture of the wetted region. In terms of the optical analog, neglecting capillarity is equivalent to using geometrical optics, with coherent shadows projected to infinity. The paper deals specifically with steady infiltration from circular cylindrical and spherical cavities. The asymptotic methods prove remarkably accurate, even far from the limit. The results replace, and explain, previous semiempirical estimates of the limiting behavior. One notable result is that the depth of the penumbra (effectively wetted region) for the cylinder is 128 times the depth for the sphere, confirming and supplementing previous studies. An odd byproduct is that we correct a long‐standing classical result in scattering theory. The scope for extending these methods to flows in other geometries, to heterogeneous soils, and generally to linear convection‐diffusion processes, is indicated br

ISSN:0043-1397    

DOI:10.1029/WR021i012p01875

年代:1985

数据来源: WILEY

摘要:

In the theory of the scattering of plane harmonic waves by an obstacle Van de Hulst theorems give simple connections between the forward scattering function and the total extinction cross section. In this paper analogous theorems are proved for two‐ and three‐dimensional quasi‐linear steady flows in saturated soils from finite cavities of arbitrary size and shape, with arbitrary boundary conditions on the cavity surface. These theorems connect “downward wetting functions” and total cavity flow rates. Simple relations are established between scattering functions in the wave context and wetting functions in the soil water context. The important consequence is that flow rates for a large range of cavity shapes can be inferred simply and directly from extant results on forward scattering functions. It is proved that at larger(dimensionless radius), flow is concentrated in a small angular region vertically beneath the cavity and has a Gaussian distribution with angular standard deviation (sr)−½(s=½αl; α, sorptive number;l, characteristic

ISSN:0043-1397    

DOI:10.1029/WR021i012p01889

年代:1985

数据来源: WILEY

摘要:

A simple and relatively rapid method of determining the characteristic or typical slope of a basin is proposed. The expression for the parameter which is given bySavg= [L(Hsu−Hso2)]/(Acos β) was developed from considerations of basin geometry and basic geomorphologic facts and involves only quantities that can be easily extracted from topographic maps. Characteristic basin slope values of 19 Appalachian Plateau watersheds which range in size from 7.4 to 178.2 km2were determined by the proposed method. These values were compared with corresponding values obtained by Horton's intersection line method and with those derived from county soil survey reports and maps. The comparisons showed very close agreement between the three sets of values indicating the high accuracy of the method developed here. Similar comparisons involving values determined by previous slope methods indicated that these values are at best poorly related to actual average basin slope, and that most of them are incapable of detecting small differences in slope between similar watersheds. Moreover, the proposed method significantly reduces the amount of work required by other slope methods of comparable accura

ISSN:0043-1397    

DOI:10.1029/WR021i012p01895

年代:1985

数据来源: WILEY