Journal of Hydraulic Engineering

Geostatistics offers a variety of tools that can be used in ground‐water estimation problems, including interpolation, integration, and differentiation. This paper introduces the basic concepts of geostatistics and its proposed linear and nonlinear estimation (kriging) techniques. These techniques view a regionalized variable as one of many possible outcomes of a random function. The spatial variability of the natural phenomenon is characterized by covariance or semivariogram functions, which are the central elements in the estimation techniques, known as simple kriging, ordinary kriging, universal kriging, log‐kriging, disjunctive kriging, and indicator kriging. The paper also discusses techniques that have been developed to infer the statistical structure of the variables of interest.

Geostatistical techniques are useful tools for analyzing the inherent uncertainties of ground‐water systems. These procedures have been applied to a variety of estimation problems in geohydrology. This paper reviews these applications in five major categories, including: (1) Mapping of ground‐water variables, incorporation of relevant information, and space‐time mapping; (2) conditional and unconditional simulations of geohydrological fields; (3) cointerpolation of groundwater variables using the flow equations, and numerical and analytical approaches to estimate cross and direct covariances of these variables based on ground‐water‐flow equations; (4) global and local sampling designs; and (5) geostatistical ground‐water‐management studies. The paper also includes a comprehensive list of geostatistical and related publications in geohydrology.

In hydraulic and hydrologic design and analysis, engineers frequently face uncertainties involving quantities that cannot be assessed with absolute accuracy. Under such circumstances, uncertainty analysis is undertaken to examine the effects of uncertain factors on the results of design and analysis. The paper introduces a mathematical technique called the Mellin transform. The technique is analytically convenient in determining the exact statistical moments of a random variable that is a function of several nonnegative independent random variables in a multiplicative form. Two examples are given to demonstrate the application of the Mellin transform to uncertainty analysis of hydrologic and hydraulic problems.

A computational methodology is described for establishing the approximate minimum‐cost engineering design for the initial construction and subsequent capacity expansion of a linear water‐supply pipeline along a specified route. Dynamic programming algorithms are utilized to determine an optimal solution to an approximation of the complete design problem. The selected design specifies the number and size of pump stations and the length, diameter, and pressure class of the pipe, including the addition of parallel pipe, to be added at the beginning of each staging interval over a planning period. Variations in pipe pressure class and the addition of parallel pipe are allowed along the individual sections of the pipeline route. This approximate least‐cost design is the optimal design if parallel pipe is not allowed. The use of the algorithm is illustrated for a potential water conveyance pipeline in the San Antonio River Basin in Texas.

Emergent wetland vegetation frequently provides most of the resistance to flow of surface water. Stems are typically spaced many diameters apart. Therefore, fluid friction should be computed from drag on single objects, not channel or packed bed equations. Complication arises from vertical variation of vegetation density and nonoriented spatial variation of soil elevations. Further, flows are often in the transition region between laminar and turbulent; and the Manning equation is therefore not appropriate. A detailed approach requires knowledge of statistical distributions of wetland ground elevation, depth, and velocity. Ground slopes are typically in the range of 0.1–100 cm/km. However, the depth range is small, so the combined effects recorrelate to a simple power law equation for dense emergent vegetation with spatial uniformity on the scale of 10 m. Parameters in the model can be estimated with sufficient accuracy from vegetation and soil surveys, combined with relatively little hydrologic data. Data from several studies are examined from this perspective.

Laboratory experiments were conducted to study various aspects of the mechanics of self‐formed, stable, straight alluvial channels in the presence of bed‐load transport. The assumptions used for the formulation of the turbulent diffusion model of Parker (1978) were examined first. Velocity measurements indicated that the logarithmic law for rough walls is a valid approximation to the velocity profile, along normals to the boundary for the whole channel depth. The equivalent sand‐grain roughness, $k_s\text{,}$ is about ${\mathrm{2d}}_{90}\text{.}$ The experiments show that the turbulent‐diffusion model is more realistic for flow in a straight channel than the threshold‐channel model. Regime relations based on the straight‐channel model, and a resistance equation, predict accurately the center depth and the top width of a self‐formed straight channel. The shape of the bank is found to follow closely an empirically fitted exponential function that requires knowledge of only the center‐channel depth. Data obtained from other studies support the findings of the present work.