Journal of Irrigation and Drainage Engineering

Overland flow of water over a porous bed in two spatial dimensions is governed by three partial differential equations accounting for continuity of momentum in the x‐ and y‐directions and continuity of mass. A leapfrog explicit finite‐difference numerical scheme was applied to solve this system of equations for the initial and boundary conditions that characterize level‐basin irrigation. The numerical procedure is stable and robust for different applications, and can accommodate three different inflow configurations: line, corner, and fan. These configurations simulate inflow from an overflowing canal on a field boundary and at point sources from a corner or in the middle of a straight boundary, respectively. A numerical test was performed to assess the effect of grid fineness on the results of the simulation and on central‐processing‐unit time requirement. Data from two field tests were used to validate the model in quasi—one‐dimensional and two‐dimensional conditions.

The development of a two‐dimensional hydrodynamic simulation model of basin irrigation is reported in a companion paper. This article presents four applications of the model. Two hypothetical case studies are used to illustrate the ability of the model to accommodate multiple inflows and irregular field shapes including internal high spots. The model is applied to study the effect of field shape on irrigation performance. The particular case of a rectangular basin irrigated from a corner is considered. Results show that one‐dimensional models can underestimate the time of advance by up to 20%. Finally, the model is applied to explore the effects of spatially varied infiltration on irrigation performance. A series of infiltration observation points is used to estimate the infiltration rate in unmeasured locations. The model is used to simulate a hypothetical case study involving the design of a square level‐basin irrigation field with spatially varied infiltration irrigated from a corner. Results show that irrigation performance changes dramatically with the location of the corner inflow.

This study presents the experimental results of one‐dimensional unsaturated water infiltration under two conditions: vertical columns of homogeneous soil and vertical columns of two‐layered soil. The purpose was to more accurately identify the movement of the wetting front under both conditions. The results showed that air pressure buildup was more pronounced in soil columns of two layers than in soil columns of one homogenous layer. Water content in the top layer of a closed two‐layer column was greater than the corresponding height in a homogeneous one‐layer column. Flow conditions and pressure buildup in the bottom layer retarded the wetting front at the interface until pressure reached a maximum value in the bottom layer. An analytical model was developed that predicts the cumulative infiltration into the top layer as well as the travel time of the wetting front.

In this study, a number of theoretical improvements were made to the finite‐element formulation for modeling three‐dimensional steady and unsteady ground‐water flow. First, the Galerkin method was combined with the collocation method to handle the time‐derivative term of the governing equation. Second, the resulting system of ordinary differential equations was solved by using finite integration. The principal directions of the anisotropy are not required to parallel the user‐selected global coordinate directions. Also, more detailed treatments to leaky boundaries, surface flux boundaries, nonhomogeneous and anisotropic aquifers, and sources/sinks are presented. The improved formulation was coded in FORTRAN. Four example cases were used to verify the model. It was found that the model is stable, accurate, and numerically oscillation free if proper time‐step size is used. A critical review of the commonly used finite‐difference solution scheme is given. A detailed discussion of how to obtain accurate numerical solutions while avoiding numerical oscillation is presented.

The Stable Slope and Sediment Transport (SSAST) model, an event‐based computer model, uses postmine hydrology and median overburden grain size of a reclaimed surface mine to calculate a stable slope for the longitudinal channel profile. Peak discharge, which drives postmine erosion, is calculated from a 10‐year, 24‐h storm using the Soil Conservation Service curve‐number method and curve numbers (CNs) calibrated for Pennsylvania surface mines. Reclaimed mine sites may be represented by either a rectangle or triangle that most closely fits the site shape and has the same drainage area and length. Sediment‐transport and slope‐stability algorithms use a modified Bagnold's equation with a correction factor dependent on particle shape. SSAST was calibrated and verified using data from three reclaimed Pennsylvania surface mines. Analyses indicate that SSAST can predict stable longitudinal channel profiles for reclamation of surface mines in the humid, temperate Northeastern United States. Disequilibrium among slope form, surface hydrology, and erosional process on reclaimed surface coal mines can cause gully erosion and sediment loads that are significantly elevated above natural values.

Flow paths to drain laterals are needed to identify local flow to drains and regional flow. This paper describes the depths at which the flow paths of the regional aquifer‐flow system and the local saturated ground‐water‐flow system separate in a field with 15 drain laterals. The finite difference ground‐water computer model MODFLOW was used to create a transient, two‐dimensional ground‐water‐flow model. Seventy‐eight piezometers were installed at various depths in the field for use in model parameter estimation and to calibrate the model. The hydraulic‐head distribution and advective velocity vectors up to 20 days after a flood irrigation event were modeled. Results confirm that the irrigation water mixes with the shallow ground water and that there is a significant downward flux of water after an irrigation event that reverses with time to a dominant lateral flow with some upward flux of regional‐water flow from a depth of 1–1.5 m below the drain laterals.

Normal depth is an important parameter occurring in the design of irrigation canals. Direct analytic solution of normal‐depth problems is not possible, as the governing equations for the practical canal sections are implicit. The solution requires tedious methods of trial and error. Tabular and graphical methods also available for solution are subject to errors of double interpolation and errors of judgment in reading the graphs. Furthermore, the methods are based on Manning's equation, which is valid for a hydraulically rough boundary having a narrow range of relative roughness and involves a roughness coefficient having awkward dimensions. Reported herein are explicit equations for normal depth in various irrigation‐canal sections.

In practice, canals located on ridges seldom have symmetric drainages on either side. In this paper, exact solution of the problem of seepage from a canal in a homogeneous medium to asymmetric drains located at finite distance from the canal is presented. The problem is solved by the use of conformal mapping. Equations for seepage discharge and the shape of the free surface are given. The values of seepage discharge are given in the form of easy to use curves. The analysis indicates that the seepage losses increase with increase in bed width and decrease in distance and the lowering of the level of the drainages. If the level of the higher drainage is raised beyond a critical value, this drainage becomes ineffective and seepage to this drainage will be zero. Fee surface rises if drainage on the other side is located at a farther and/or at a higher level.

The main advantages of gunite brow ditches are cost, ease of construction, durability, and simple flow‐capacity equations. The main disadvantages are weakness due to shrinkage cracks; rigidity, which makes them vulnerable to soils movement; susceptibility to chemical attack; aesthetics; and maintenance, which is required to keep them clear of obstruction that can clog pathways. The standard specifications require a setback from the top‐of‐slope of 0.3 m (12 in.). This setback should be adequate for slopes in rock and for compacted sands and gravels. But slopes composed of compacted clay will creep if the slope face is wet to saturated. The three parameters that determine the primary zone of creep for this condition are shear strength, slope height, and slope inclination. An empirical equation [(1)] can be used to estimate the gunite brow ditch top‐of‐slope setback distance for compacted‐clay slopes.

In the traditional analysis, the radius is defined as a constant radial distance beyond which the aquifer is undisturbed by the pumping of water from a well. In the real world, the radius is a transient variable. Its value is zero when the pumping starts, and it expands radially in the aquifer as pumping proceeds. A transient radius of influence is a proper concept to describe well hydraulics. Traditional analyses in well hydraulics were focused on water table drawdown, and less attention was given to the cone of depression volume. From the conservation of mass principle, the cone of depression volume is related to the amount of water removed from the aquifer and is, therefore, related to the pumping time. Such an concept is employed to obtain transient solutions of well drawdown and radius of influence for a well in an unconfined aquifer under a constant recharge rate.

Starting and maintaining windbreaks are especially important in arid and semiarid agricultural areas. To evaluate which of several species of trees might be most appropriate for windbreaks in various environments, a factorial block experiment using three types of soil, five different qualities of irrigation water, and three common species of windbreak tree seedlings for arid climates was conducted to measure the effects of soil type and water quality on tree survival and growth. The three species of trees were used: prosopis, Prosopis juliflora; eucalyptus, Eucalyptus camaldulensis; and casuarina (sometimes called horsetail beefwood), Casuarina equisetifolia. The results showed prosopis to be the most salt‐tolerant. The best soil for saline irrigation water depended on the species of tree, but for prosopis, the sandy soil proved more desirable. If leaching were applied, sandy soils would probably be better in all circumstances. Prosopis survived, though did not grow well, with water up to 8,600 parts per million of total dissolved solids.

The investigation deals with conveyance efficiency and global hydraulic efficiency in Spanish irrigation systems. The values of conveyance efficiency are calculated for five channels. As the lack of reliable data makes it impossible to calculate global efficiency, a method is developed that is based on the comparison between the theoretical crop water requirements and the volume released at the head of the main channel. The so‐defined net demand/release ratio marks the upper limit of global efficiency. Values are calculated in 38 irrigation systems that represent about a fifth of the total irrigated surface in Spain. It is demonstrated that the most water loss occurs in distribution and application. Analysis of the influence of diverse system characteristics, such as irrigation method, gross supply, water prices, and tariff types shows the importance of these aspects on irrigation efficiency.